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      "source": [
        "# <center> Lecture10 : Evaluating Regression Models </center>  \n",
        " \n",
        "## <center> Instructor: Dr. Hu Chuan-Peng </center> "
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        "* 在lec9中，我们已经学习了使用一个简单的线性模型来拟合变量间的关系。但这并未结束，接下来，我们需要对模型进行**评估**  \n",
        "\n",
        "* 我们可以从以下三个角度来思考这个问题：  \n",
        "\n",
        "    1. 模型本身公正吗？(How fair is the model?)  \n",
        "\n",
        "    2. 模型存在错误吗？(How wrong is the model?)  \n",
        "\n",
        "    3. 后验预测模型有多准确？(How accurate are the posterior predictive models?)  \n"
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      "source": [
        "## 模型公正吗(Is the model fair?)  \n",
        "\n",
        "模型公正性是一个上位概念，它描述了模型是否符合我们(社会、道德、伦理)的预期，而不仅是关注模型和样本数据的关系。  \n",
        "\n",
        "我们可以借助几个相关问题来理解和思考模型的公众性：  \n",
        "\n",
        "1. 数据的收集过程是怎样的？  \n",
        "\n",
        "2. 数据由谁收集，数据收集的目的是什么？  \n",
        "\n",
        "3. 数据收集的过程，以及分析的结果，将对个人和社会产生什么影响？  \n",
        "\n",
        "4. 分析过程中可能会包含哪些偏见  \n",
        "    * p-hacking/HARKing"
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        "**结合上节课的例子来思考这几个问题**  \n",
        "\n",
        "上节课我们发现，压力可以负向预测自我控制。  \n",
        "\n",
        "* 也就是说，压力越大，自我控制就越差。  \n",
        "\n",
        "![Image Name](https://cdn.kesci.com/upload/s3y4rmsym1.png?imageView2/0/w/960/h/960)  \n"
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        "**1. 数据的收集的过程公平吗？**  \n",
        "\n",
        "在本示例研究中，数据来自于被试在问卷上提供的信息。  \n",
        "\n",
        "* 数据收集过程是公平的，被试自愿完成问卷，并获得相应的报酬。  \n",
        "* 此外，数据收集过程是匿名化的，保护了被试的隐私。  \n",
        "\n",
        "一些极端的反例：  \n",
        "* 在收集数据时，仅考察了大学生被试，而没有考虑其他人群(比如中国的中小学生)。  \n",
        "* 在衡量压力大小时，我们通过剥夺被试的睡眠来给被试施加压力。  \n",
        "\n",
        "🤔基于这些数据的模型公正吗？  \n",
        "\n",
        "> * 压力量表来源：Cohen, S., Kamarck, T. & Mermelstein, R. A global measure of perceived stress. J. Health. Soc. Behav. 24, 385–396 (1983).  \n",
        "> * 自我控制量表来源：Tangney, J. P., Baumeister, R. F. & Boone, A. L. High self-control predicts good adjustment, less pathology, better grades, and interpersonal success. J. Pers. 72, 271–324 (2004)."
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        "**2. 研究目的，以及数据收集的目的公平吗？**  \n",
        "\n",
        "在本示例研究中，研究目的来源自心理学家的好奇和假设。这是合理的，因为心理学研究是一种探索性的研究方法。  \n",
        "\n",
        "一个极端的反例：  \n",
        "* 如果研究项目来源于开发缓解压力药的厂商。那么，研究目的就可能被操纵，以支持药厂的销售。  \n",
        "* 例如，有目的的选择本身就具有疾病的患者进行实验。  \n",
        "* 例如，有目的性的将压力对自我控制的影响夸大，制造消费者的恐慌情绪。"
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        "**3. 模型分析的结果，将对个人和社会产生什么影响？**  \n",
        "\n",
        "在本示例研究中，研究结果(模型分析的结果)具有一定的理论意义和实际意义。  \n",
        "* 在理论层面，压力对自我控制的影响可能反应了自我功能的特性。  \n",
        "* 在实际意义层面，这可以为自我控制的干预提供指导。  \n",
        "\n",
        "一个极端的反例：  \n",
        "* 例如，在司法领域中工程师开发了一种风险评估和分类模型，该模型可以评估是否拘留还是释放当事人。  \n",
        "* 即使模型使用的数据是公正的，并且模型在技术上是有效的，但是该模型在几乎在所有情况下都建议拘留当事人。"
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        "**4. 分析过程中包含的偏见？**  \n",
        "\n",
        "在本示例研究中，我们关注一个简单的线性模型，并通过回归系数来反映压力与自我控制的关系。  \n",
        "\n",
        "一些反例：  \n",
        "* 假设在一次研究中使用多种问卷收集多种因变量，然后选择有相关性的变量进行报告?  \n",
        "* 在多因素实验设计中，通过增加变量来获得显著的交互作用，并尝试多种简单效应分析。"
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        "此外，在心理学研究中，模型公正性往往与***心理学研究的可重复性***相关。  \n",
        "\n",
        "1. 数据的收集过程是怎样的？  \n",
        "\n",
        "2. 数据由谁收集，数据收集的目的是什么？  \n",
        "\n",
        "3. 数据收集的过程，以及分析的结果，将对个人和社会产生什么影响？  \n",
        "\n",
        "4. 分析过程中可能会包含哪些偏见  \n",
        "    * p-hacking/HARKing  \n",
        "\n",
        "![Image Name](https://pic2.zhimg.com/80/v2-778de6c621356bc2c23c3a09ff2b0be5_1440w.webp)  \n",
        "(来源：胡传鹏, ..., 彭凯平. (2016). 心理学研究中的可重复性问题:从危机到契机. 心理科学进展(9), 15.)"
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        "## 这个模型可能有多错误(How wrong is the model?)  \n",
        "\n",
        ">  **<center>“all models are wrong, but some are useful.   ————George Box”</center>**  \n",
        "\n",
        "\n",
        "* 尽管统计模型是对更复杂现实的简化表达，良好的统计模型仍然可以是有用的，并可以增进我们对世界复杂性的理解。  \n",
        "\n",
        "* 因此，在评估模型时，要问的下一个问题不是模型是否错误(is the model wrong?)，而是模型错误的程度(How wrong is the model?)  \n",
        "\n",
        "让我们回到lec9的例子中，🤔思考贝叶斯线性回归模型的假设在多大程度上与现实相符？"
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        "### 模型假设的影响  \n",
        "\n",
        "**🤔 我们知道模型存在前提预设(assumption)，如果这些模型的前提预设不成立，模型会变得多糟糕？**  \n",
        "\n",
        "在lec9中，我们使用一个线性模型来定义压力分数与自我控制分数之间的关系，并且指定了该模型成立的一些前提预设。  \n",
        "\n",
        "$$  \n",
        "\\begin{align*}  \n",
        "Y_i &= \\beta_0 + \\beta_1 X_i + \\epsilon \\;\\;\\;\\;\\;\\;\\;\\;\\epsilon \\sim N(0,\\sigma^2)\\\\  \n",
        "&\\Downarrow \\\\  \n",
        "Y_i | \\beta_0, \\beta_1, \\sigma &\\stackrel{ind}{\\sim} N\\left(\\mu_i, \\sigma^2\\right) \\;\\; \\text{ with } \\;\\; \\mu_i = \\beta_0 + \\beta_1X_i  .\\\\  \n",
        "\\end{align*}  \n",
        "$$  \n",
        "\n",
        "* 回归模型需满足如下假设：  \n",
        "\n",
        "    1. 独立观测假设: 每个观测值$Y_i$是相互独立的，即一个观测的值不受其他观测的影响.  \n",
        "\n",
        "    2. 线性关系假设: 预测值$\\mu_i$和自变量$X_i$之间可以用线性关系来描述，即：$\\mu_i = \\beta_0 + \\beta_1 X_i$.  \n",
        "\n",
        "    3. 方差同质性假设: 在任意自变量的取值下，观测值$Y_i$都会以$\\mu_i$为中心，同样的标准差$\\sigma$呈正态分布变化（$\\sigma$ is consistent）.  \n",
        "\n",
        "![Image Name](https://cdn.kesci.com/upload/s3y4rmsym1.png?imageView2/0/w/960/h/960)  \n",
        "\n"
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        "**1. 当假设1(独立观测假设)被违反时：**  \n",
        "\n",
        "* 在心理学的实验数据当中，很多时候观测值之间存在依赖关系(dependent)。  \n",
        "* 比如，反应时在单个被试内、或某种特定刺激类型内可能更同质：有的被试总是反应得比其他人更快，有的刺激总是能导致更快的反应。  \n",
        "* 这时，被试内/项目内反应时数据的相互关联会导致对于结果的错误估计。  \n",
        "\n",
        "* 我们在之后会学习使用层级贝叶斯模型来处理相互关联的数据。  \n",
        "\n",
        "![Image Name](https://cdn.kesci.com/upload/s3xt2u50rw.png?imageView2/0/w/960/h/960)  \n",
        "\n",
        "> source: Brown, V. A. (2021). An Introduction to Linear Mixed-Effects Modeling in R. Advances in Methods and Practices in Psychological Science, 4(1), 2515245920960351. https://doi.org/10.1177/2515245920960351"
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        "**2. 当假设2(线性关系假设)和假设3(方差同质性假设)被违反时：**  \n",
        "\n",
        "* 假设2(线性关系假设)违反的情况：在左图中，我们可以看到，Y和X之间的关系并非线性的  \n",
        "\n",
        "* 假设3(方差同质性假设)违反的情况：并且，随着X的增大，Y的变异性越来越大。  \n",
        "\n",
        "  * 这要导致的后果是，后验预测分布比实际观测值的分布差异很大(右图)  \n",
        "\n",
        "![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/nonlinear-1-ch10-1.png)  \n",
        "\n"
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        "### 对模型进行修改  \n",
        "\n",
        "* 考虑到并不是所有数据都会满足这些假设，当这些假设被违反时，我们需要考虑修改模型。"
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      "source": [
        "对于违反假设1 的情况，我们在之后会学习使用层级贝叶斯模型来处理相互关联的数据。  \n",
        "\n",
        "**对于违反假设2和3的情况，通常有两种处理方式**  \n",
        "\n",
        "**a. 使用不同的数据模型**  \n",
        "\n",
        "* 不假设实际值与观测值之间的关系是正态的  $Y_i \\sim N(\\mu_i, \\sigma^2)$  \n",
        "\n",
        "* 之后，我们会学习使用其他回归模型来描述其数据关系，比如泊松回归、二项回归、负二项回归。  \n"
      ]
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        "**b. 对数据进行变换**  \n",
        "\n",
        "> 如果数据模型并不是我们要担心的问题，我们可以对数据进行变换，仍然可以对变换后的数据可以使用正态模型：  \n",
        "\n",
        "* 对$Y$进行变换：$g(Y_i) | \\beta_0, \\beta_1, \\sigma \\stackrel{ind}{\\sim}N(\\mu_i, \\sigma^2)$，$\\mu_i = \\beta_0 + \\beta_1 X_i$  \n",
        "\n",
        "* 对$X$进行变换： $Y_i | \\beta_0, \\beta_1, \\sigma \\stackrel{ind}{\\sim}N(\\mu_i, \\sigma^2)$，$\\mu_i = \\beta_0 + \\beta_1 h(X_i)$  \n",
        "\n",
        "* 同时对$Y$和$X$进行变换：$g(Y_i) | \\beta_0, \\beta_1, \\sigma \\stackrel{ind}{\\sim}N(\\mu_i, \\sigma^2)$， $\\mu_i = \\beta_0 + \\beta_1 h(X_i)$"
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      "source": [
        "在刚刚的例子当中，我们对$Y$的取值做一个对数变换  \n",
        "\n",
        "$$  \n",
        "\\log(Y_i) | \\beta_0, \\beta_1, \\sigma \\stackrel{ind}{\\sim}N(\\mu_i, \\sigma^2) \\;\\; \\text{ with } \\; \\mu_i = \\beta_0 + \\beta_1 X_i  \n",
        "$$  \n",
        "\n",
        "* 在变换之后，可以看到$\\log(Y)$与$X$之间的关系仍然是线性的，且随着$X$的增大，$Y$的变异性仍然是一致的。  \n",
        "\n",
        "* 可以使用正态的线性模型来拟合$\\log(Y)$的后验分布  \n",
        "* 这部分内容将在逻辑回归(logistic regression)部分进行详细介绍，这里先不作深入解释。  \n",
        "\n",
        "<table>  \n",
        "        <tr>  \n",
        "            <td><img src=\"https://www.bayesrulesbook.com/bookdown_files/figure-html/nonlinear-1-ch10-1.png\" alt=\"\" width=\"500\" height=\"250\"></td>  \n",
        "            <td><img src=\"https://www.bayesrulesbook.com/bookdown_files/figure-html/nonlinear-2-ch10-1.png\" alt=\"\" width=\"500\" height=\"250\"></td>  \n",
        "        </tr>  \n",
        "        <tr>  \n",
        "            <td>变换之前</td>  \n",
        "            <td>log变换之后</td>  \n",
        "        </tr>  \n",
        "</table>  \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F3E21ED945404810AB3684B65FD58D0B",
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      "source": [
        "## 模型评估  \n",
        "\n",
        "一般情况下，我们的贝叶斯模型不会是完全不公平的，或者错得太离谱的。 但除了这些问题，**更为重要的是，模型是否可以用来准确预测新数据 Y 的结果。**  \n",
        "\n",
        "> 如果说模型公平性和模型错误描述的是模型在**质量上**的优劣，那模型评估与比较就是在**数量上**衡量模型预测的准确性。  \n",
        "\n",
        "接下来我们讲介绍衡量后验预测的两种指标：  \n",
        "- 绝对误差的中位数，median absolute error (MAE)  \n",
        "- 后验预测区间，posterior prediction interval"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B321E583F4494566887D5A946EE37CB4",
        "jupyter": {},
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      "source": [
        "### Median absolute error (MAE)  \n",
        "\n",
        "绝对误差的中位数，median absolute error (MAE)衡量了预测观测值$Y_i$与后验预测均值之间$Y_i'$的差异。  \n",
        "\n",
        "$$  \n",
        "\\text{MAE} = median\\left(|Y_i - \\hat{Y}_i|\\right)  \n",
        "$$  \n",
        "\n",
        "- 假设 $Y_1, Y_2…, Y_n$表示n个观察结果。  \n",
        "\n",
        "- 每个 $Y_i$ 都有对应的后验预测值，其均值为 $Y_i'$  \n",
        "\n",
        "结合我们之前的例子来理解绝对误差的中位数：  \n",
        "- 首先，以压力 $X_i=45$ 下的后验预测值为例。  \n",
        "\n",
        "- 其次，计算后验预测的均值和观测值之间的误差。  \n",
        "\n",
        "- 再次，计算所有自变量下，后验预测均值和观测值之间的误差。  \n",
        "\n",
        "- 最后，计算所有误差的中位数。  \n",
        "\n",
        "![Image Name](https://cdn-media-1.freecodecamp.org/images/MNskFmGPKuQfMLdmpkT-X7-8w2cJXulP3683)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "68869553A1C14F50B3EAD5B67D3ED75C",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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      "source": [
        "**（知识回顾）首先，我们考虑压力 $X_i=45$ 下的后验预测模型**  \n",
        "\n",
        "1. 读取数据 Data_Sum_HPP_Multi_Site_Share，选择\"Tsinghua\"站点的数据作为示例。  \n",
        "\n",
        "2. 使用 **PyMC** 对压力变量`stress` 和自我控制变量 `scontrol` 建立回归模型。  \n",
        "\n",
        "3. 在模型拟合后(略过模型诊断环境)，生成模型的后验预测。  \n",
        "\n",
        "4. 最后，计算压力 $X_i=45$条件下，后验预测均值和观测值之间的误差。  \n",
        "\n",
        "*(注：由于压力分数为45时，存在多个自我控制分数与之对应，我们从中随机抽取一个作为演示)*"
      ]
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      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n"
          ]
        }
      ],
      "source": [
        "# 导入 pymc 模型包，和 arviz 等分析工具 \n",
        "import pymc as pm\n",
        "import arviz as az\n",
        "import seaborn as sns\n",
        "import scipy.stats as st\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import xarray as xr\n",
        "import pandas as pd\n",
        "\n",
        "# 忽略不必要的警告\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
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      "source": [
        "# 通过 pd.read_csv 加载数据 Data_Sum_HPP_Multi_Site_Share.csv\n",
        "try:\n",
        "  df_raw = pd.read_csv('/home/mw/input/bayes20238001/Data_Sum_HPP_Multi_Site_Share.csv')\n",
        "except:\n",
        "  df_raw = pd.read_csv('data/Data_Sum_HPP_Multi_Site_Share.csv')\n",
        "\n",
        "\n",
        "# 筛选站点为\"Tsinghua\"的数据\n",
        "df = df_raw[df_raw[\"Site\"] == \"Tsinghua\"]\n",
        "\n",
        "# 选择需要的两列\n",
        "df = df[[\"stress\",\"scontrol\"]]\n",
        "\n",
        "#设置索引\n",
        "df[\"index\"] = range(len(df))\n",
        "df = df.set_index(\"index\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "id": "BE38DAFFABC14B49889F1EC7C4C16B99",
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        {
          "name": "stdout",
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          "text": [
            "       stress  scontrol\n",
            "index                  \n",
            "123        45        35\n"
          ]
        }
      ],
      "source": [
        "# 从压力值为45对应的自我控制分数中随机抽取一个，并标记其索引号\n",
        "# 我们将根据该索引号来提取对应的后验预测值\n",
        "print(df[df.stress == 45].sample(n=1, random_state=84735))"
      ]
    },
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      "execution_count": 6,
      "metadata": {
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        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
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      "source": [
        "# 对压力变量`stress` 和自我控制变量 `scontrol` 建立回归模型\n",
        "with pm.Model() as linear_model:\n",
        "\n",
        "    beta_0 = pm.Normal(\"beta_0\", mu=70, sigma=4)          #定义beta_0          \n",
        "    beta_1 = pm.Normal(\"beta_1\", mu=0, sigma=0.8)         #定义beta_1\n",
        "    sigma = pm.Exponential(\"sigma\", 0.6)                  #定义sigma\n",
        "\n",
        "    #x是自变量压力水平\n",
        "    x = pm.MutableData(\"x\", df.stress, dims=\"obs_id\")       \n",
        "    #定义mu，讲自变量与先验结合\n",
        "    mu = pm.Deterministic(\"mu\", beta_0 + beta_1 * x, dims=\"obs_id\")    \n",
        "    #定义似然：预测值y符合N(mu, sigma)分布, observed 为传入实际数据y 自我控制水平\n",
        "    likelihood = pm.Normal(\"y_est\", mu=mu, sigma=sigma, observed=df.scontrol, dims=\"obs_id\")   "
      ]
    },
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      "execution_count": 7,
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        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Auto-assigning NUTS sampler...\n",
            "Initializing NUTS using jitter+adapt_diag...\n",
            "Multiprocess sampling (4 chains in 4 jobs)\n",
            "NUTS: [beta_0, beta_1, sigma]\n"
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            "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 29 seconds.\n"
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        }
      ],
      "source": [
        "# 模型拟合 \n",
        "#===========================\n",
        "#     注意！！！以下代码可能需要运行1-2分钟左右\n",
        "#===========================\n",
        "with linear_model:\n",
        "    trace = pm.sample(draws=5000,                   # 使用mcmc方法进行采样，draws为采样次数\n",
        "                      tune=1000,                    # tune为调整采样策略的次数，可以决定这些结果是否要被保留\n",
        "                      chains=4,                     # 链数\n",
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        "                      random_seed=84735)"
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            "Sampling: [y_est]\n"
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        "# 进行后验预测采样\n",
        "with linear_model:\n",
        "    ppc = pm.sample_posterior_predictive(trace,\n",
        "                                         random_seed=84735)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D88A4FC18C2F492EA5DB5B66D6E86B39",
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        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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      "source": [
        "**计算预测误差(prediction error)**  \n",
        "\n",
        "接下来，我们从`ppc`中提取压力 $X_i=45$条件下的生成的后验预测，并计算后验预测的均值和观测值之间的误差(prediction error)。  \n",
        "\n",
        "- 查看 `ppc`，可以发现其中存储了`posterior_predictive`，`observed_data`，`constant_data`  \n",
        "    - 生成的后验预测存储在`posterior_predictive`中  \n",
        "\n",
        "    - `observed_data`对应原始数据集中的因变量，自我控制分数(df.scontrol)  \n",
        "    \n",
        "    - `constant_data`对应原始数据集中的自变量，压力分数(df.scontrol)  \n",
        "\n",
        "- 之前提取出的自变量$X_i=45$，其对应的索引为123，我们将利用这个索引提取存储在`ppc`中对应的真实值、对应的后验预测值"
      ]
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              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-index-preview {\n",
              "  grid-column: 2 / 5;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data,\n",
              ".xr-index-data-in:checked ~ .xr-index-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-index-name div,\n",
              ".xr-index-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 4, draw: 5000, obs_id: 174)\n",
              "Coordinates:\n",
              "  * chain    (chain) int32 0 1 2 3\n",
              "  * draw     (draw) int32 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "  * obs_id   (obs_id) int32 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    y_est    (chain, draw, obs_id) float64 36.92 27.44 48.72 ... 37.68 42.96\n",
              "Attributes:\n",
              "    created_at:                 2023-11-14T12:25:07.003262\n",
              "    arviz_version:              0.14.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.1</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-5978ed7d-3a65-42e2-a32e-89ef591e0f0f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5978ed7d-3a65-42e2-a32e-89ef591e0f0f' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-9bed6845-f4e1-4314-86eb-8e3bd32af509' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9bed6845-f4e1-4314-86eb-8e3bd32af509' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-8f17e61f-a6ca-4429-bf55-9320cf3edee0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8f17e61f-a6ca-4429-bf55-9320cf3edee0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c150a9fd-6b8b-4b89-b85c-2003a45534fc' class='xr-var-data-in' type='checkbox'><label for='data-c150a9fd-6b8b-4b89-b85c-2003a45534fc' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-774e9414-b1e8-407e-ae12-7a8e737a492c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-774e9414-b1e8-407e-ae12-7a8e737a492c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5f9e4403-8b3c-4c9b-a0c3-4bcd7e29cc82' class='xr-var-data-in' type='checkbox'><label for='data-5f9e4403-8b3c-4c9b-a0c3-4bcd7e29cc82' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-7c534567-1070-41a4-acbe-d107880c3898' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7c534567-1070-41a4-acbe-d107880c3898' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4901a116-1392-433a-83e1-0b0c2097538d' class='xr-var-data-in' type='checkbox'><label for='data-4901a116-1392-433a-83e1-0b0c2097538d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-98b80ffa-5792-49ad-aa8c-eb6b7925da2c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-98b80ffa-5792-49ad-aa8c-eb6b7925da2c' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(chain, draw, obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>36.92 27.44 48.72 ... 37.68 42.96</div><input id='attrs-e6ebe48b-5bb3-4e16-813a-136f1b93d023' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e6ebe48b-5bb3-4e16-813a-136f1b93d023' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3a55adbc-59c6-4687-bb05-0a8870f8481b' class='xr-var-data-in' type='checkbox'><label for='data-3a55adbc-59c6-4687-bb05-0a8870f8481b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[36.92276684, 27.44345169, 48.7222452 , ..., 29.46240585,\n",
              "         39.48126999, 41.10724944],\n",
              "        [49.7123554 , 41.57957662, 43.19495065, ..., 27.66144214,\n",
              "         38.76727372, 43.41906542],\n",
              "        [44.63972334, 36.83831604, 55.65196249, ..., 38.62367501,\n",
              "         44.20300424, 42.40432794],\n",
              "        ...,\n",
              "        [29.65160796, 35.08907743, 45.8700571 , ..., 32.56881772,\n",
              "         40.86351258, 40.55296736],\n",
              "        [45.70373672, 35.85786763, 50.00985845, ..., 34.72535898,\n",
              "         39.32089265, 45.93337016],\n",
              "        [47.21680853, 42.59284653, 48.14909209, ..., 45.89817211,\n",
              "         29.12116789, 38.27040516]],\n",
              "\n",
              "       [[49.0821512 , 37.36535136, 41.04873798, ..., 28.00006555,\n",
              "         28.79360388, 46.45111245],\n",
              "        [45.90492109, 45.49137644, 46.01579295, ..., 38.26239835,\n",
              "         45.64096285, 44.44047316],\n",
              "        [37.55170547, 48.16406598, 48.52640762, ..., 42.70676328,\n",
              "         41.73714803, 43.70585225],\n",
              "...\n",
              "        [42.50862074, 43.18428506, 42.6588589 , ..., 34.19253396,\n",
              "         43.08749388, 43.49472737],\n",
              "        [44.40865644, 41.30343371, 51.01470526, ..., 43.80868315,\n",
              "         43.31742782, 41.78400625],\n",
              "        [36.80214962, 39.31001772, 41.63192978, ..., 31.60405655,\n",
              "         47.46169698, 40.09994246]],\n",
              "\n",
              "       [[44.43465779, 39.64245217, 45.72254567, ..., 37.88691367,\n",
              "         40.22244854, 57.31967379],\n",
              "        [49.13113199, 26.63785269, 48.10218176, ..., 40.60777707,\n",
              "         37.75974866, 44.70295162],\n",
              "        [43.80315515, 38.2271946 , 41.4231897 , ..., 32.92058566,\n",
              "         46.13443142, 33.91538262],\n",
              "        ...,\n",
              "        [33.17154301, 34.62641527, 41.51661958, ..., 32.71129583,\n",
              "         43.75933667, 44.91628828],\n",
              "        [32.86387633, 45.67367414, 50.95752644, ..., 38.79152986,\n",
              "         36.93799299, 52.7017916 ],\n",
              "        [32.1573863 , 42.16505783, 39.6287242 , ..., 33.25336391,\n",
              "         37.6756042 , 42.95946613]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5e313be7-61a2-48ff-b5ce-a04003bce286' class='xr-section-summary-in' type='checkbox'  ><label for='section-5e313be7-61a2-48ff-b5ce-a04003bce286' class='xr-section-summary' >Indexes: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-5eb97c19-981f-47b5-b9af-4f6b60bcc209' class='xr-index-data-in' type='checkbox'/><label for='index-5eb97c19-981f-47b5-b9af-4f6b60bcc209' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([0, 1, 2, 3], dtype=&#x27;int32&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-453dd333-e4ea-4a19-9aae-9e381c6ee98b' class='xr-index-data-in' type='checkbox'/><label for='index-453dd333-e4ea-4a19-9aae-9e381c6ee98b' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
              "       ...\n",
              "       4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999],\n",
              "      dtype=&#x27;int32&#x27;, name=&#x27;draw&#x27;, length=5000))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>obs_id</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-0f4e5a18-e6b7-4921-aa6d-eaab4062b9ec' class='xr-index-data-in' type='checkbox'/><label for='index-0f4e5a18-e6b7-4921-aa6d-eaab4062b9ec' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
              "       ...\n",
              "       164, 165, 166, 167, 168, 169, 170, 171, 172, 173],\n",
              "      dtype=&#x27;int32&#x27;, name=&#x27;obs_id&#x27;, length=174))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3177d197-7fe9-4104-a1e5-55de7e088972' class='xr-section-summary-in' type='checkbox'  checked><label for='section-3177d197-7fe9-4104-a1e5-55de7e088972' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-14T12:25:07.003262</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.1</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_observed_datab036d819-bc23-4ae2-9a49-79705ee00b55\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_observed_datab036d819-bc23-4ae2-9a49-79705ee00b55\" class = \"xr-section-summary\">observed_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body[data-theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-index-preview {\n",
              "  grid-column: 2 / 5;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data,\n",
              ".xr-index-data-in:checked ~ .xr-index-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-index-name div,\n",
              ".xr-index-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
              ".xr-index-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 174)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int32 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    y_est    (obs_id) float64 47.0 40.0 40.0 46.0 50.0 ... 33.0 35.0 38.0 39.0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-14T12:25:07.004280\n",
              "    arviz_version:              0.14.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.1</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-0c039e19-a06a-4078-8440-99c1604db17b' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-0c039e19-a06a-4078-8440-99c1604db17b' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-21d1cc4a-c770-4a24-a59e-ef62e4f80cd1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-21d1cc4a-c770-4a24-a59e-ef62e4f80cd1' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-d8a1ab48-f828-4986-aa4b-8129fb5be1a9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d8a1ab48-f828-4986-aa4b-8129fb5be1a9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4c55328b-7075-440d-8a07-8022f6768d2c' class='xr-var-data-in' type='checkbox'><label for='data-4c55328b-7075-440d-8a07-8022f6768d2c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-cddc1500-dce6-4b2e-87a7-c80398e0f538' class='xr-section-summary-in' type='checkbox'  checked><label for='section-cddc1500-dce6-4b2e-87a7-c80398e0f538' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>47.0 40.0 40.0 ... 35.0 38.0 39.0</div><input id='attrs-fa3b009f-d150-4057-ae02-9fa389774f60' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fa3b009f-d150-4057-ae02-9fa389774f60' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d2969c36-995a-4261-802d-9bfea41e3acd' class='xr-var-data-in' type='checkbox'><label for='data-d2969c36-995a-4261-802d-9bfea41e3acd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([47., 40., 40., 46., 50., 43., 36., 35., 47., 50., 44., 34., 26.,\n",
              "       42., 48., 41., 46., 43., 40., 52., 46., 41., 46., 40., 42., 41.,\n",
              "       48., 49., 46., 35., 37., 45., 37., 36., 35., 45., 35., 40., 35.,\n",
              "       49., 39., 38., 45., 40., 37., 36., 42., 32., 40., 45., 33., 45.,\n",
              "       42., 40., 23., 32., 50., 44., 40., 36., 28., 51., 40., 33., 29.,\n",
              "       37., 38., 38., 26., 40., 41., 43., 44., 38., 34., 46., 43., 42.,\n",
              "       43., 40., 33., 44., 38., 40., 43., 31., 51., 50., 42., 41., 34.,\n",
              "       38., 37., 42., 41., 27., 46., 33., 35., 48., 39., 41., 43., 31.,\n",
              "       40., 38., 43., 38., 36., 41., 48., 44., 28., 36., 32., 42., 30.,\n",
              "       40., 43., 36., 38., 25., 41., 35., 36., 45., 35., 36., 33., 42.,\n",
              "       28., 43., 44., 38., 31., 33., 29., 43., 47., 42., 48., 27., 36.,\n",
              "       31., 48., 34., 40., 32., 46., 34., 39., 36., 37., 39., 47., 44.,\n",
              "       37., 40., 50., 35., 42., 24., 38., 41., 45., 35., 44., 46., 39.,\n",
              "       52., 33., 35., 38., 39.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ad02a410-876a-429d-b254-0b5ec18cf3c6' class='xr-section-summary-in' type='checkbox'  ><label for='section-ad02a410-876a-429d-b254-0b5ec18cf3c6' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>obs_id</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-cda9f3e0-a0e5-46e9-92c9-ed3cab501092' class='xr-index-data-in' type='checkbox'/><label for='index-cda9f3e0-a0e5-46e9-92c9-ed3cab501092' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
              "       ...\n",
              "       164, 165, 166, 167, 168, 169, 170, 171, 172, 173],\n",
              "      dtype=&#x27;int32&#x27;, name=&#x27;obs_id&#x27;, length=174))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-701fe4a9-0159-4d82-90bc-e428f56bf377' class='xr-section-summary-in' type='checkbox'  checked><label for='section-701fe4a9-0159-4d82-90bc-e428f56bf377' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-14T12:25:07.004280</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.1</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_constant_data56a8f227-04f6-4fd3-a8de-03f257374383\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_constant_data56a8f227-04f6-4fd3-a8de-03f257374383\" class = \"xr-section-summary\">constant_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
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              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
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              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
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              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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              "\n",
              "html[theme=dark],\n",
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              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
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              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
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              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
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              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
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              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
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              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
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              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-item input:enabled + label {\n",
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              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              "\n",
              ".xr-section-summary {\n",
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              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
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              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-summary-in + label:before {\n",
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              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
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              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
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              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
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              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
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              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
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              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
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              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
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              "\n",
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              "\n",
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              "\n",
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              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
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              "\n",
              ".xr-index-preview {\n",
              "  grid-column: 2 / 5;\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
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              ".xr-var-dims,\n",
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              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
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              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
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              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
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              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
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              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data,\n",
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              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
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              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-index-name div,\n",
              ".xr-index-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
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              ".xr-var-attrs,\n",
              ".xr-var-data,\n",
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              "  grid-column: 1 / -1;\n",
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              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 174)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int32 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    x        (obs_id) int32 38 43 31 35 45 42 41 58 ... 29 36 43 32 42 42 39 33\n",
              "Attributes:\n",
              "    created_at:                 2023-11-14T12:25:07.004280\n",
              "    arviz_version:              0.14.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.1</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-95efef09-5da5-4b73-8238-55f6e71ae188' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-95efef09-5da5-4b73-8238-55f6e71ae188' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-870e0fc8-af17-43fb-b750-5502a4544254' class='xr-section-summary-in' type='checkbox'  checked><label for='section-870e0fc8-af17-43fb-b750-5502a4544254' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-376af210-f064-4eb0-9bdb-5202cd28c9e6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-376af210-f064-4eb0-9bdb-5202cd28c9e6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3a5dab0e-8ec2-4350-8143-9c5e310f27e2' class='xr-var-data-in' type='checkbox'><label for='data-3a5dab0e-8ec2-4350-8143-9c5e310f27e2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f35b2dea-56bc-425f-a217-cb0bf73100b7' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f35b2dea-56bc-425f-a217-cb0bf73100b7' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>38 43 31 35 45 ... 32 42 42 39 33</div><input id='attrs-1f9f38c6-9a3c-4d97-ace1-0d5c8c48298f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1f9f38c6-9a3c-4d97-ace1-0d5c8c48298f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0dbe8378-098a-4044-a872-e32574699896' class='xr-var-data-in' type='checkbox'><label for='data-0dbe8378-098a-4044-a872-e32574699896' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([38, 43, 31, 35, 45, 42, 41, 58, 47, 33, 40, 34, 45, 38, 31, 40, 37,\n",
              "       36, 37, 38, 35, 34, 44, 44, 36, 36, 39, 40, 30, 47, 35, 48, 42, 42,\n",
              "       40, 35, 36, 28, 47, 27, 49, 41, 37, 37, 41, 49, 54, 50, 36, 43, 35,\n",
              "       33, 40, 39, 39, 46, 26, 49, 36, 42, 43, 33, 46, 46, 51, 43, 38, 44,\n",
              "       49, 26, 31, 50, 47, 42, 46, 36, 40, 33, 33, 50, 43, 30, 36, 37, 30,\n",
              "       42, 39, 46, 39, 28, 52, 26, 43, 38, 38, 46, 39, 44, 41, 44, 42, 30,\n",
              "       39, 45, 46, 38, 36, 42, 39, 41, 37, 32, 49, 40, 42, 43, 48, 47, 35,\n",
              "       44, 35, 48, 38, 45, 34, 30, 35, 45, 42, 32, 39, 38, 33, 35, 36, 36,\n",
              "       46, 43, 26, 34, 37, 44, 41, 50, 22, 43, 41, 57, 43, 45, 39, 43, 41,\n",
              "       57, 35, 43, 39, 38, 33, 55, 38, 46, 42, 48, 26, 40, 29, 36, 43, 32,\n",
              "       42, 42, 39, 33])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f140ac0e-52f3-491e-9132-c16a349d8a0a' class='xr-section-summary-in' type='checkbox'  ><label for='section-f140ac0e-52f3-491e-9132-c16a349d8a0a' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>obs_id</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-78d70263-19e7-4f24-bc00-7ec5281d48ee' class='xr-index-data-in' type='checkbox'/><label for='index-78d70263-19e7-4f24-bc00-7ec5281d48ee' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,\n",
              "       ...\n",
              "       164, 165, 166, 167, 168, 169, 170, 171, 172, 173],\n",
              "      dtype=&#x27;int32&#x27;, name=&#x27;obs_id&#x27;, length=174))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5c372db2-1fd3-4cc5-aa71-3f97bb143468' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5c372db2-1fd3-4cc5-aa71-3f97bb143468' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-14T12:25:07.004280</dd><dt><span>arviz_version :</span></dt><dd>0.14.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.1</dd></dl></div></li></ul></div></div><br></div>\n",
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            ],
            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior_predictive\n",
              "\t> observed_data\n",
              "\t> constant_data"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ppc"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "id": "CB8CFD0682BA43A3B970F37A36511E10",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
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        },
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        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# 确定constant_data(即自变量)中索引值为123的压力分数确实是 45\n",
        "ppc.constant_data[\"x\"][123].values == 45"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "id": "7B23A7F572AC4981A147CBD3B817F1C9",
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        "notebookId": "655b69f19f41eb29b96aa410",
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      "source": [
        "# 提取压力分数 45对应的后验预测值\n",
        "ppc_45 = ppc.posterior_predictive[\"y_est\"][:,:,123]"
      ]
    },
    {
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              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
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              "\n",
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              "\n",
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              "\n",
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              "\n",
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              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2,\n",
              ".xr-no-icon {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;y_est&#x27; (chain: 4, draw: 5000)&gt;\n",
              "array([[25.62745617, 37.16025268, 35.30988842, ..., 42.16571322,\n",
              "        33.80591645, 42.97840258],\n",
              "       [31.42623034, 37.66481206, 33.88059608, ..., 44.61889487,\n",
              "        25.3808912 , 28.49703366],\n",
              "       [38.8057164 , 37.94139232, 43.3455127 , ..., 45.5561559 ,\n",
              "        42.35256263, 36.14129823],\n",
              "       [41.07574935, 37.73826936, 36.64628003, ..., 39.8585858 ,\n",
              "        32.35338851, 29.56510791]])\n",
              "Coordinates:\n",
              "  * chain    (chain) int32 0 1 2 3\n",
              "  * draw     (draw) int32 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "    obs_id   int32 123</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'y_est'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-5203bb62-8c01-476b-acf2-8c1a8a3b0015' class='xr-array-in' type='checkbox' checked><label for='section-5203bb62-8c01-476b-acf2-8c1a8a3b0015' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>25.63 37.16 35.31 39.69 45.51 44.21 ... 33.92 38.07 39.86 32.35 29.57</span></div><div class='xr-array-data'><pre>array([[25.62745617, 37.16025268, 35.30988842, ..., 42.16571322,\n",
              "        33.80591645, 42.97840258],\n",
              "       [31.42623034, 37.66481206, 33.88059608, ..., 44.61889487,\n",
              "        25.3808912 , 28.49703366],\n",
              "       [38.8057164 , 37.94139232, 43.3455127 , ..., 45.5561559 ,\n",
              "        42.35256263, 36.14129823],\n",
              "       [41.07574935, 37.73826936, 36.64628003, ..., 39.8585858 ,\n",
              "        32.35338851, 29.56510791]])</pre></div></div></li><li class='xr-section-item'><input id='section-71fc4a72-6ba8-47fa-8b99-09f2bc106955' class='xr-section-summary-in' type='checkbox'  checked><label for='section-71fc4a72-6ba8-47fa-8b99-09f2bc106955' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-4ff1222a-62ba-45a4-8aae-c62d05ee2cbb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4ff1222a-62ba-45a4-8aae-c62d05ee2cbb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d465a292-db4b-4a35-aa49-66ab3bb74d5e' class='xr-var-data-in' type='checkbox'><label for='data-d465a292-db4b-4a35-aa49-66ab3bb74d5e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-dbbfcbbf-9483-49e2-8674-53e7c35ab5c3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-dbbfcbbf-9483-49e2-8674-53e7c35ab5c3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-79240d43-491a-4ab7-9b75-2f668d627523' class='xr-var-data-in' type='checkbox'><label for='data-79240d43-491a-4ab7-9b75-2f668d627523' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>obs_id</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>123</div><input id='attrs-f1390185-a7ed-46b3-b3d8-39607d0e5f0e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f1390185-a7ed-46b3-b3d8-39607d0e5f0e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3eac21ca-0923-48e3-a587-99e51290f7f0' class='xr-var-data-in' type='checkbox'><label for='data-3eac21ca-0923-48e3-a587-99e51290f7f0' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(123)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-08ab1eb8-33fe-48b4-989a-cad64a17d229' class='xr-section-summary-in' type='checkbox'  ><label for='section-08ab1eb8-33fe-48b4-989a-cad64a17d229' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-3ca3f614-f728-4da2-8d90-017afae03bbb' class='xr-index-data-in' type='checkbox'/><label for='index-3ca3f614-f728-4da2-8d90-017afae03bbb' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([0, 1, 2, 3], dtype=&#x27;int32&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-d678cf5d-d8f6-41b6-93a1-5d2f3ae08c68' class='xr-index-data-in' type='checkbox'/><label for='index-d678cf5d-d8f6-41b6-93a1-5d2f3ae08c68' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
              "       ...\n",
              "       4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999],\n",
              "      dtype=&#x27;int32&#x27;, name=&#x27;draw&#x27;, length=5000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5ba1e093-70dc-4e37-9dcf-1550047c36e9' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5ba1e093-70dc-4e37-9dcf-1550047c36e9' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
            ],
            "text/plain": [
              "<xarray.DataArray 'y_est' (chain: 4, draw: 5000)>\n",
              "array([[25.62745617, 37.16025268, 35.30988842, ..., 42.16571322,\n",
              "        33.80591645, 42.97840258],\n",
              "       [31.42623034, 37.66481206, 33.88059608, ..., 44.61889487,\n",
              "        25.3808912 , 28.49703366],\n",
              "       [38.8057164 , 37.94139232, 43.3455127 , ..., 45.5561559 ,\n",
              "        42.35256263, 36.14129823],\n",
              "       [41.07574935, 37.73826936, 36.64628003, ..., 39.8585858 ,\n",
              "        32.35338851, 29.56510791]])\n",
              "Coordinates:\n",
              "  * chain    (chain) int32 0 1 2 3\n",
              "  * draw     (draw) int32 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "    obs_id   int32 123"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ppc_45"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6BE03BFAE4BA4D51975E50E71450C460",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "**计算后验预测的均值:**  \n",
        "\n",
        "- 提取所有 链(chain:4)和 采样次数(4*5000)下，的后验预测值  \n",
        "\n",
        "- 计算平均值  \n",
        "\n",
        "- 结果显示，在压力 $X_i=45$时，后验预测(自我控制得分)的均值为36.9"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
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      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "prediction error: 36.918902941687314\n"
          ]
        }
      ],
      "source": [
        "ppc_45_mean = ppc_45.stack(sample=(\"chain\", \"draw\")).mean().values\n",
        "\n",
        "print(\"prediction error:\", ppc_45_mean)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8B66840B319C4A1EB6BF98678A39A0DE",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "**计算后验预测均值和观测值之间的误差**  \n",
        "\n",
        "我们看一下在压力 $X_i=45$时，原数据中的自我控制分数  \n",
        "\n",
        "然后，进一步计算后验预测误差(prediction error)。  \n",
        "- $\\text{prediction error} = Y-Y'$  \n",
        "\n",
        "- 即观测值$(Y)$和后验预测均值$(Y')$之间的误差。"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
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        "id": "97F140399EB94BCCB8B4840A3EB4A9CC",
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        "notebookId": "655b69f19f41eb29b96aa410",
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Observed Value(X=45): 35.0\n"
          ]
        }
      ],
      "source": [
        "print(\"Observed Value(X=45):\",ppc.observed_data[\"y_est\"][123].values)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
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        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
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        "tags": [],
        "trusted": true
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "prediction error: -1.918902941687314\n"
          ]
        }
      ],
      "source": [
        "# 提取观测数据\n",
        "true_y = ppc.observed_data[\"y_est\"][123].values\n",
        "\n",
        "# 获得预测模型的均值\n",
        "pre_y_mean = ppc_45_mean\n",
        "\n",
        "# 计算后验预测误差\n",
        "pre_error = true_y - pre_y_mean\n",
        "print(\"prediction error:\", pre_error)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9C25D6E9D4C548E1A12D2EACF69C9397",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "**计算所有观测变量下后验预测模型的均值和观测值之间的误差**  \n",
        "\n",
        "\n",
        "\n",
        "$$  \n",
        "\\begin{array}{lll}  \n",
        "\\text{Markov chain parameter sets} & & \\text{Simulated posterior predictive models} \\\\  \n",
        "\\left[  \n",
        "\\begin{array}{lll}  \n",
        "\\beta_0^{(1)} & \\beta_1^{(1)} & \\sigma^{(1)} \\\\  \n",
        "\\hline  \n",
        "\\beta_0^{(2)} & \\beta_1^{(2)} & \\sigma^{(2)} \\\\  \n",
        "\\hline  \n",
        "\\vdots & \\vdots & \\vdots \\\\  \n",
        "\\hline  \n",
        "\\beta_0^{(20000)} & \\beta_1^{(20000)} & \\sigma^{(20000)} \\\\  \n",
        "\\end{array}  \n",
        "\\right]  \n",
        "& \\; \\longrightarrow \\;  \n",
        "& \\left[  \n",
        "\\begin{array}{l|l|l|l}  \n",
        "Y_1^{(1)} & Y_2^{(1)} & \\cdots & Y_{174}^{(1)} \\\\  \n",
        "Y_1^{(2)} & Y_2^{(2)} & \\cdots & Y_{174}^{(2)} \\\\  \n",
        "\\vdots & \\vdots &  & \\vdots \\\\  \n",
        "Y_1^{(20000)} & Y_2^{(20000)} & \\cdots & Y_{174}^{(20000)} \\\\  \n",
        "\\end{array}  \n",
        "\\right]  \n",
        "\\end{array}  \n",
        "\n",
        "$$  \n",
        "\n",
        "* 在当前数据集中，自变量共有`174`个  \n",
        "\n",
        "* 因此，相对于之前我们仅考虑 $X_i=45$ 时的单一情况，现在我们可以计算 所有$X$取值下对应的后验预测的均值。  \n",
        "\n",
        "  * 代入`20000`个参数对，每个自变量都拥有对应的20000个后验预测值  \n",
        "\n",
        "  * 对于每个$X$，计算后验预测的均值  \n",
        "\n",
        "  * 进而，计算每个$X$下，后验预测均值和观测值之间的误差  \n",
        "\n",
        "![Image Name](https://cdn-media-1.freecodecamp.org/images/MNskFmGPKuQfMLdmpkT-X7-8w2cJXulP3683)  \n",
        "\n",
        "资料来源：https://www.freecodecamp.org/news/machine-learning-mean-squared-error-regression-line-c7dde9a26b93/"
      ]
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              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;y_est&#x27; (chain: 4, draw: 5000, obs_id: 174)&gt;\n",
              "array([[[37.17928622, 26.98226507, 49.90507747, ..., 29.15132464,\n",
              "         39.83179059, 41.79911201],\n",
              "        [49.17884201, 40.60248473, 42.92529399, ..., 26.46296462,\n",
              "         37.95914918, 43.04134461],\n",
              "        [44.12856608, 36.273458  , 55.21917594, ..., 38.07751015,\n",
              "         43.72080748, 41.5922247 ],\n",
              "        ...,\n",
              "        [30.81905244, 35.56341664, 45.78583365, ..., 33.31537037,\n",
              "         40.94832677, 40.8900699 ],\n",
              "        [44.85905922, 35.96239992, 48.73922393, ..., 34.93553305,\n",
              "         39.08652819, 45.05557962],\n",
              "        [46.99660879, 42.43470429, 47.46189327, ..., 45.89091776,\n",
              "         27.73549683, 37.0572504 ]],\n",
              "\n",
              "       [[49.36445521, 37.93724032, 41.49223021, ..., 28.78552014,\n",
              "         29.54991112, 46.77650779],\n",
              "        [46.66767795, 46.51453661, 46.38961224, ..., 38.85276683,\n",
              "         46.44636293, 44.84504182],\n",
              "        [38.62356186, 50.69913222, 50.23194441, ..., 44.60292732,\n",
              "         43.31584756, 45.0553892 ],\n",
              "...\n",
              "        [42.72839636, 43.28034965, 43.0241022 , ..., 34.5373706 ,\n",
              "         43.2713028 , 43.79617922],\n",
              "        [43.66511777, 40.7236543 , 49.89061319, ..., 43.06994767,\n",
              "         42.63813397, 41.26049574],\n",
              "        [37.09684265, 39.64349381, 41.00761416, ..., 32.67667397,\n",
              "         46.71104257, 39.75396418]],\n",
              "\n",
              "       [[42.78286292, 38.34838403, 44.22095517, ..., 36.84721693,\n",
              "         39.03293796, 54.33830171],\n",
              "        [48.82541634, 26.88475394, 47.36051818, ..., 40.64579572,\n",
              "         37.63592973, 44.12419868],\n",
              "        [43.81625484, 38.86094454, 41.41020442, ..., 33.96155172,\n",
              "         45.98649695, 34.58731663],\n",
              "        ...,\n",
              "        [33.53733419, 34.36293246, 42.45918396, ..., 32.62125852,\n",
              "         43.69755566, 45.52457825],\n",
              "        [33.58336838, 45.13866273, 51.22329994, ..., 38.77243183,\n",
              "         37.31382425, 52.67308152],\n",
              "        [32.72375452, 41.73460936, 40.29641465, ..., 33.43859207,\n",
              "         37.83074102, 43.26893527]]])\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1 2 3\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'y_est'</div><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-c966f610-d668-41e6-a6b5-ef0aebe9e33c' class='xr-array-in' type='checkbox' checked><label for='section-c966f610-d668-41e6-a6b5-ef0aebe9e33c' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>37.18 26.98 49.91 47.05 42.51 51.78 ... 50.33 35.31 33.44 37.83 43.27</span></div><div class='xr-array-data'><pre>array([[[37.17928622, 26.98226507, 49.90507747, ..., 29.15132464,\n",
              "         39.83179059, 41.79911201],\n",
              "        [49.17884201, 40.60248473, 42.92529399, ..., 26.46296462,\n",
              "         37.95914918, 43.04134461],\n",
              "        [44.12856608, 36.273458  , 55.21917594, ..., 38.07751015,\n",
              "         43.72080748, 41.5922247 ],\n",
              "        ...,\n",
              "        [30.81905244, 35.56341664, 45.78583365, ..., 33.31537037,\n",
              "         40.94832677, 40.8900699 ],\n",
              "        [44.85905922, 35.96239992, 48.73922393, ..., 34.93553305,\n",
              "         39.08652819, 45.05557962],\n",
              "        [46.99660879, 42.43470429, 47.46189327, ..., 45.89091776,\n",
              "         27.73549683, 37.0572504 ]],\n",
              "\n",
              "       [[49.36445521, 37.93724032, 41.49223021, ..., 28.78552014,\n",
              "         29.54991112, 46.77650779],\n",
              "        [46.66767795, 46.51453661, 46.38961224, ..., 38.85276683,\n",
              "         46.44636293, 44.84504182],\n",
              "        [38.62356186, 50.69913222, 50.23194441, ..., 44.60292732,\n",
              "         43.31584756, 45.0553892 ],\n",
              "...\n",
              "        [42.72839636, 43.28034965, 43.0241022 , ..., 34.5373706 ,\n",
              "         43.2713028 , 43.79617922],\n",
              "        [43.66511777, 40.7236543 , 49.89061319, ..., 43.06994767,\n",
              "         42.63813397, 41.26049574],\n",
              "        [37.09684265, 39.64349381, 41.00761416, ..., 32.67667397,\n",
              "         46.71104257, 39.75396418]],\n",
              "\n",
              "       [[42.78286292, 38.34838403, 44.22095517, ..., 36.84721693,\n",
              "         39.03293796, 54.33830171],\n",
              "        [48.82541634, 26.88475394, 47.36051818, ..., 40.64579572,\n",
              "         37.63592973, 44.12419868],\n",
              "        [43.81625484, 38.86094454, 41.41020442, ..., 33.96155172,\n",
              "         45.98649695, 34.58731663],\n",
              "        ...,\n",
              "        [33.53733419, 34.36293246, 42.45918396, ..., 32.62125852,\n",
              "         43.69755566, 45.52457825],\n",
              "        [33.58336838, 45.13866273, 51.22329994, ..., 38.77243183,\n",
              "         37.31382425, 52.67308152],\n",
              "        [32.72375452, 41.73460936, 40.29641465, ..., 33.43859207,\n",
              "         37.83074102, 43.26893527]]])</pre></div></div></li><li class='xr-section-item'><input id='section-fd8f97ea-fba9-453b-a35f-28a877728e2f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-fd8f97ea-fba9-453b-a35f-28a877728e2f' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-6bfd7781-3bbc-4fcd-adb2-774e1d57002b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6bfd7781-3bbc-4fcd-adb2-774e1d57002b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-68e1ca99-3532-4b86-8362-cd3db1b6d2fe' class='xr-var-data-in' type='checkbox'><label for='data-68e1ca99-3532-4b86-8362-cd3db1b6d2fe' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-098eb45e-423d-48b8-96bd-c2a0433b2467' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-098eb45e-423d-48b8-96bd-c2a0433b2467' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6882733c-e2a4-4d94-8460-9d1164a275ab' class='xr-var-data-in' type='checkbox'><label for='data-6882733c-e2a4-4d94-8460-9d1164a275ab' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-55beafd1-8eec-4c8d-bd85-c96983e6cc0c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-55beafd1-8eec-4c8d-bd85-c96983e6cc0c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f6ef5b07-a59a-4d9f-b6be-cdc0d02f5e16' class='xr-var-data-in' type='checkbox'><label for='data-f6ef5b07-a59a-4d9f-b6be-cdc0d02f5e16' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ba88cc6c-9e3f-4602-a9b2-acfe9a1e4bfd' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-ba88cc6c-9e3f-4602-a9b2-acfe9a1e4bfd' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
            ],
            "text/plain": [
              "<xarray.DataArray 'y_est' (chain: 4, draw: 5000, obs_id: 174)>\n",
              "array([[[37.17928622, 26.98226507, 49.90507747, ..., 29.15132464,\n",
              "         39.83179059, 41.79911201],\n",
              "        [49.17884201, 40.60248473, 42.92529399, ..., 26.46296462,\n",
              "         37.95914918, 43.04134461],\n",
              "        [44.12856608, 36.273458  , 55.21917594, ..., 38.07751015,\n",
              "         43.72080748, 41.5922247 ],\n",
              "        ...,\n",
              "        [30.81905244, 35.56341664, 45.78583365, ..., 33.31537037,\n",
              "         40.94832677, 40.8900699 ],\n",
              "        [44.85905922, 35.96239992, 48.73922393, ..., 34.93553305,\n",
              "         39.08652819, 45.05557962],\n",
              "        [46.99660879, 42.43470429, 47.46189327, ..., 45.89091776,\n",
              "         27.73549683, 37.0572504 ]],\n",
              "\n",
              "       [[49.36445521, 37.93724032, 41.49223021, ..., 28.78552014,\n",
              "         29.54991112, 46.77650779],\n",
              "        [46.66767795, 46.51453661, 46.38961224, ..., 38.85276683,\n",
              "         46.44636293, 44.84504182],\n",
              "        [38.62356186, 50.69913222, 50.23194441, ..., 44.60292732,\n",
              "         43.31584756, 45.0553892 ],\n",
              "...\n",
              "        [42.72839636, 43.28034965, 43.0241022 , ..., 34.5373706 ,\n",
              "         43.2713028 , 43.79617922],\n",
              "        [43.66511777, 40.7236543 , 49.89061319, ..., 43.06994767,\n",
              "         42.63813397, 41.26049574],\n",
              "        [37.09684265, 39.64349381, 41.00761416, ..., 32.67667397,\n",
              "         46.71104257, 39.75396418]],\n",
              "\n",
              "       [[42.78286292, 38.34838403, 44.22095517, ..., 36.84721693,\n",
              "         39.03293796, 54.33830171],\n",
              "        [48.82541634, 26.88475394, 47.36051818, ..., 40.64579572,\n",
              "         37.63592973, 44.12419868],\n",
              "        [43.81625484, 38.86094454, 41.41020442, ..., 33.96155172,\n",
              "         45.98649695, 34.58731663],\n",
              "        ...,\n",
              "        [33.53733419, 34.36293246, 42.45918396, ..., 32.62125852,\n",
              "         43.69755566, 45.52457825],\n",
              "        [33.58336838, 45.13866273, 51.22329994, ..., 38.77243183,\n",
              "         37.31382425, 52.67308152],\n",
              "        [32.72375452, 41.73460936, 40.29641465, ..., 33.43859207,\n",
              "         37.83074102, 43.26893527]]])\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1 2 3\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ppc.posterior_predictive[\"y_est\"]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "id": "36C247C99CF342D994FD31332B5F6F3D",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>stress</th>\n",
              "      <th>scontrol_ppc_mean</th>\n",
              "      <th>scontrol_original</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>index</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>38</td>\n",
              "      <td>40.456385</td>\n",
              "      <td>47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>43</td>\n",
              "      <td>37.973829</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>31</td>\n",
              "      <td>44.033258</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>35</td>\n",
              "      <td>42.083939</td>\n",
              "      <td>46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>45</td>\n",
              "      <td>36.941873</td>\n",
              "      <td>50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>42</td>\n",
              "      <td>38.459205</td>\n",
              "      <td>43</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>41</td>\n",
              "      <td>38.950593</td>\n",
              "      <td>36</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>58</td>\n",
              "      <td>30.351497</td>\n",
              "      <td>35</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>47</td>\n",
              "      <td>35.916818</td>\n",
              "      <td>47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>33</td>\n",
              "      <td>43.085859</td>\n",
              "      <td>50</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       stress  scontrol_ppc_mean  scontrol_original\n",
              "index                                              \n",
              "0          38          40.456385                 47\n",
              "1          43          37.973829                 40\n",
              "2          31          44.033258                 40\n",
              "3          35          42.083939                 46\n",
              "4          45          36.941873                 50\n",
              "5          42          38.459205                 43\n",
              "6          41          38.950593                 36\n",
              "7          58          30.351497                 35\n",
              "8          47          35.916818                 47\n",
              "9          33          43.085859                 50"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# 提取出所有的后验预测值，每一个X对应4*5000个后验预测值，使用stack汇总到一起\n",
        "pre_per_x = ppc.posterior_predictive[\"y_est\"].stack(sample=(\"chain\", \"draw\"))\n",
        "\n",
        "#计算均值\n",
        "pre_y_mean = pre_per_x.mean(axis=1).values\n",
        "\n",
        "# 提取自变量X，对应的观测值Y、后验预测均值，存放在一个表格中\n",
        "pre_y_mean = pd.DataFrame({\n",
        "    \"stress\": df.stress,\n",
        "    \"scontrol_ppc_mean\": pre_y_mean,\n",
        "    \"scontrol_original\": df.scontrol\n",
        "})\n",
        "\n",
        "#显示表格前10行\n",
        "pre_y_mean.head(10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "037D69B6E3BF4D9093115BDF77018A41",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "**计算所有误差的中位数(MAE)**  \n",
        "\n",
        "$$  \n",
        "{\\mathsf{MAE}}={\\mathsf{median}}|Y_{i}-Y_{i}^{\\prime}|.  \n",
        "$$  \n",
        "\n",
        "- MAE 为所有预测误差Y-Y'的绝对值的中位数。  \n",
        "\n",
        "最后，我们计算所有观测值与后验预测模型均值之间的误差。"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "id": "19B45CDB1C9E421980D81B616C94449E",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "计算得到的MAE: 3.59\n"
          ]
        }
      ],
      "source": [
        "from statistics import median\n",
        "\n",
        "# 计算预测误差的绝对值\n",
        "pre_y_mean[\"pre_error\"] = abs(pre_y_mean[\"scontrol_original\"] - pre_y_mean[\"scontrol_ppc_mean\"])\n",
        "\n",
        "# 最后，计算预测误差的中位数\n",
        "MAE = median(pre_y_mean.pre_error)\n",
        "print(f\"计算得到的MAE: {MAE:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "id": "EF5AA0609DBD449D8D18D7BE478462D2",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<Axes: title={'center': 'x'}>"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# 可视化预测误差MAE\n",
        "pre_error = pre_y_mean.pre_error.values\n",
        "az.plot_posterior(pre_error, hdi_prob=0.95, point_estimate=\"median\", ref_val=MAE)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6DFEE96D5E364877B76531FE5E507AAE",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "对于 MAE 的解读。  \n",
        "\n",
        "- 绝对误差的中位数，median absolute error (MAE)衡量了预测观测值$Y_i$与后验预测均值之间$Y_i'$的差异。  \n",
        "- **MAE越小**表明后验模型的**预测越准确**。  \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6620FD9EA9DB49078B7D9018195ED86A",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "### 后验预测区间，posterior prediction interval  \n",
        "\n",
        "- MAE 是一个有效的指标，可以衡量模型对于样本观测值的预测能力。  \n",
        "\n",
        "- 然而，MAE 仅考虑了后验预测误差的中位数，而不是其可信区间。  \n",
        "\n",
        "- 后验预测区间(posterior prediction interval)则进一步反应了样本观测值与后验预测可信区间的关系。  \n",
        "\n",
        "![Image Name](https://cdn.kesci.com/upload/s3xt34m35o.png?imageView2/0/w/700/h/700)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8E67D08CB2C34B8EA01541034CD16F8D",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "为了便于理解，我们还是回到仅考虑$X_i=45$的情况。  \n",
        "\n",
        "- MCMC采样针对该$X_i$生成了20000个后验预测值  \n",
        "- 我们可以用`az.summary`快速查看这20000个后验预测值的情况，包括均值和可信区间  \n",
        "\n",
        "此时, 后验预测的均值为36  \n",
        "- 并且，此时的94%可信区间为27到47.7  \n",
        "- 对比真实数据可以发现，有2个观测值(26、50)落在可信区间外。"
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              "         mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
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              "y_est    1.0  "
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              "       stress  scontrol\n",
              "index                  \n",
              "4          45        50\n",
              "12         45        26\n",
              "103        45        31\n",
              "123        45        35\n",
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        "**计算所有X下，观测值落在后验预测可信区间的情况**  \n",
        "\n",
        "\n",
        "\n",
        "$$  \n",
        "\\begin{array}{lll}  \n",
        "\\text{Markov chain parameter sets} & & \\text{Simulated posterior predictive models} \\\\  \n",
        "\\left[  \n",
        "\\begin{array}{lll}  \n",
        "\\beta_0^{(1)} & \\beta_1^{(1)} & \\sigma^{(1)} \\\\  \n",
        "\\hline  \n",
        "\\beta_0^{(2)} & \\beta_1^{(2)} & \\sigma^{(2)} \\\\  \n",
        "\\hline  \n",
        "\\vdots & \\vdots & \\vdots \\\\  \n",
        "\\hline  \n",
        "\\beta_0^{(20000)} & \\beta_1^{(20000)} & \\sigma^{(20000)} \\\\  \n",
        "\\end{array}  \n",
        "\\right]  \n",
        "& \\; \\longrightarrow \\;  \n",
        "& \\left[  \n",
        "\\begin{array}{l|l|l|l}  \n",
        "Y_1^{(1)} & Y_2^{(1)} & \\cdots & Y_{174}^{(1)} \\\\  \n",
        "Y_1^{(2)} & Y_2^{(2)} & \\cdots & Y_{174}^{(2)} \\\\  \n",
        "\\vdots & \\vdots &  & \\vdots \\\\  \n",
        "Y_1^{(20000)} & Y_2^{(20000)} & \\cdots & Y_{174}^{(20000)} \\\\  \n",
        "\\end{array}  \n",
        "\\right]  \n",
        "\\end{array}  \n",
        "\n",
        "$$  \n",
        "\n",
        "* 在当前数据集中，我们可以计算每一个X取值下，对应的后验预测可信区间。  \n",
        "\n",
        "  * 代入`20000`个参数对，每个自变量都拥有对应的`20000`个后验预测值，通过这些值获得可信区间  \n",
        "\n",
        "* 计算出`174`个可信区间之后，并观察真实值落在可信区间的情况  \n"
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        "**计算后验预测HDI**  \n",
        "\n",
        "我们先计算单个X对应的后验预测HDI，并打包为函数：  \n",
        "\n",
        "- 首先，定义函数，计算对应X下的后验预测HDI范围  \n",
        "\n",
        "- 其次，判断观测值是否超过 HDI 范围  \n",
        "\n",
        "- 最后，记录并返回超过 HDI 范围的观测值的数量"
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              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 4, draw: 5000, obs_id: 174)\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1 2 3\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    y_est    (chain, draw, obs_id) float64 37.18 26.98 49.91 ... 37.83 43.27\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:08:03.687043\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-24aede2c-7131-49ca-92e4-4ae8f186ca34' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-24aede2c-7131-49ca-92e4-4ae8f186ca34' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-3bad5c1e-714f-4be3-b568-46ad2d196be0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-3bad5c1e-714f-4be3-b568-46ad2d196be0' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-93e8c190-285c-44d3-9e34-a56dfa68ec23' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-93e8c190-285c-44d3-9e34-a56dfa68ec23' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5481ba6c-b3a0-49cb-ae1c-c99126ba4295' class='xr-var-data-in' type='checkbox'><label for='data-5481ba6c-b3a0-49cb-ae1c-c99126ba4295' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-fba81363-9569-445c-bd7e-8bcf1d960fbd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fba81363-9569-445c-bd7e-8bcf1d960fbd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e9829381-b597-43cb-93a0-65d430e4d9c9' class='xr-var-data-in' type='checkbox'><label for='data-e9829381-b597-43cb-93a0-65d430e4d9c9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-0d593575-b540-4194-bc4f-a67e8aa5f5fe' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0d593575-b540-4194-bc4f-a67e8aa5f5fe' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b101c1c2-d460-4483-8fe6-3d04c2400bfb' class='xr-var-data-in' type='checkbox'><label for='data-b101c1c2-d460-4483-8fe6-3d04c2400bfb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f8325ae2-5f93-42c6-abb3-80d39b08630c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f8325ae2-5f93-42c6-abb3-80d39b08630c' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(chain, draw, obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>37.18 26.98 49.91 ... 37.83 43.27</div><input id='attrs-5cbc6b6d-6621-4ace-80ea-018b9aaa87ec' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5cbc6b6d-6621-4ace-80ea-018b9aaa87ec' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-30cc68e0-86aa-4dcb-923f-b16dbc1dd6dd' class='xr-var-data-in' type='checkbox'><label for='data-30cc68e0-86aa-4dcb-923f-b16dbc1dd6dd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[37.17928622, 26.98226507, 49.90507747, ..., 29.15132464,\n",
              "         39.83179059, 41.79911201],\n",
              "        [49.17884201, 40.60248473, 42.92529399, ..., 26.46296462,\n",
              "         37.95914918, 43.04134461],\n",
              "        [44.12856608, 36.273458  , 55.21917594, ..., 38.07751015,\n",
              "         43.72080748, 41.5922247 ],\n",
              "        ...,\n",
              "        [30.81905244, 35.56341664, 45.78583365, ..., 33.31537037,\n",
              "         40.94832677, 40.8900699 ],\n",
              "        [44.85905922, 35.96239992, 48.73922393, ..., 34.93553305,\n",
              "         39.08652819, 45.05557962],\n",
              "        [46.99660879, 42.43470429, 47.46189327, ..., 45.89091776,\n",
              "         27.73549683, 37.0572504 ]],\n",
              "\n",
              "       [[49.36445521, 37.93724032, 41.49223021, ..., 28.78552014,\n",
              "         29.54991112, 46.77650779],\n",
              "        [46.66767795, 46.51453661, 46.38961224, ..., 38.85276683,\n",
              "         46.44636293, 44.84504182],\n",
              "        [38.62356186, 50.69913222, 50.23194441, ..., 44.60292732,\n",
              "         43.31584756, 45.0553892 ],\n",
              "...\n",
              "        [42.72839636, 43.28034965, 43.0241022 , ..., 34.5373706 ,\n",
              "         43.2713028 , 43.79617922],\n",
              "        [43.66511777, 40.7236543 , 49.89061319, ..., 43.06994767,\n",
              "         42.63813397, 41.26049574],\n",
              "        [37.09684265, 39.64349381, 41.00761416, ..., 32.67667397,\n",
              "         46.71104257, 39.75396418]],\n",
              "\n",
              "       [[42.78286292, 38.34838403, 44.22095517, ..., 36.84721693,\n",
              "         39.03293796, 54.33830171],\n",
              "        [48.82541634, 26.88475394, 47.36051818, ..., 40.64579572,\n",
              "         37.63592973, 44.12419868],\n",
              "        [43.81625484, 38.86094454, 41.41020442, ..., 33.96155172,\n",
              "         45.98649695, 34.58731663],\n",
              "        ...,\n",
              "        [33.53733419, 34.36293246, 42.45918396, ..., 32.62125852,\n",
              "         43.69755566, 45.52457825],\n",
              "        [33.58336838, 45.13866273, 51.22329994, ..., 38.77243183,\n",
              "         37.31382425, 52.67308152],\n",
              "        [32.72375452, 41.73460936, 40.29641465, ..., 33.43859207,\n",
              "         37.83074102, 43.26893527]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-02e75da2-8731-4f3c-8d90-06123c8954e2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-02e75da2-8731-4f3c-8d90-06123c8954e2' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:08:03.687043</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_observed_data9fd1697f-0b52-4515-ba16-9eaabe4293b8\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_observed_data9fd1697f-0b52-4515-ba16-9eaabe4293b8\" class = \"xr-section-summary\">observed_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
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              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
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              "\n",
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              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
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              "  --xr-background-color: var(--jp-layout-color0, white);\n",
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              "\n",
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              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
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              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
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              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
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              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
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              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
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              ".xr-section-item input + label {\n",
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              "\n",
              ".xr-section-item input:enabled + label {\n",
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              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
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              "\n",
              ".xr-section-summary > span {\n",
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              ".xr-section-summary-in:disabled + label {\n",
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              ".xr-section-summary-in:checked + label > span {\n",
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              ".xr-section-summary,\n",
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              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 174)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    y_est    (obs_id) float64 47.0 40.0 40.0 46.0 50.0 ... 33.0 35.0 38.0 39.0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:08:03.703210\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-0ab3907d-b906-44cc-8395-6532a560515b' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-0ab3907d-b906-44cc-8395-6532a560515b' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-fd9ef2e0-ed99-4a24-abff-c33f706dd603' class='xr-section-summary-in' type='checkbox'  checked><label for='section-fd9ef2e0-ed99-4a24-abff-c33f706dd603' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-330f863e-e350-45a6-979b-07bad3fa59d5' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-330f863e-e350-45a6-979b-07bad3fa59d5' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1c056d08-094d-46f7-928f-9081876e2654' class='xr-var-data-in' type='checkbox'><label for='data-1c056d08-094d-46f7-928f-9081876e2654' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3f3dcd68-87b7-4801-8a5b-06f9215af370' class='xr-section-summary-in' type='checkbox'  checked><label for='section-3f3dcd68-87b7-4801-8a5b-06f9215af370' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>47.0 40.0 40.0 ... 35.0 38.0 39.0</div><input id='attrs-741970bc-fd53-4140-8ba7-20c91980589b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-741970bc-fd53-4140-8ba7-20c91980589b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-05a72e9c-3ba7-4bd4-94c0-4312e95ecd1d' class='xr-var-data-in' type='checkbox'><label for='data-05a72e9c-3ba7-4bd4-94c0-4312e95ecd1d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([47., 40., 40., 46., 50., 43., 36., 35., 47., 50., 44., 34., 26.,\n",
              "       42., 48., 41., 46., 43., 40., 52., 46., 41., 46., 40., 42., 41.,\n",
              "       48., 49., 46., 35., 37., 45., 37., 36., 35., 45., 35., 40., 35.,\n",
              "       49., 39., 38., 45., 40., 37., 36., 42., 32., 40., 45., 33., 45.,\n",
              "       42., 40., 23., 32., 50., 44., 40., 36., 28., 51., 40., 33., 29.,\n",
              "       37., 38., 38., 26., 40., 41., 43., 44., 38., 34., 46., 43., 42.,\n",
              "       43., 40., 33., 44., 38., 40., 43., 31., 51., 50., 42., 41., 34.,\n",
              "       38., 37., 42., 41., 27., 46., 33., 35., 48., 39., 41., 43., 31.,\n",
              "       40., 38., 43., 38., 36., 41., 48., 44., 28., 36., 32., 42., 30.,\n",
              "       40., 43., 36., 38., 25., 41., 35., 36., 45., 35., 36., 33., 42.,\n",
              "       28., 43., 44., 38., 31., 33., 29., 43., 47., 42., 48., 27., 36.,\n",
              "       31., 48., 34., 40., 32., 46., 34., 39., 36., 37., 39., 47., 44.,\n",
              "       37., 40., 50., 35., 42., 24., 38., 41., 45., 35., 44., 46., 39.,\n",
              "       52., 33., 35., 38., 39.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f64ecdad-0e1c-4b27-8d0c-a1de24f4a73f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f64ecdad-0e1c-4b27-8d0c-a1de24f4a73f' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:08:03.703210</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_constant_datad1d404b2-0c02-412a-9550-83fcc1cbcee3\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_constant_datad1d404b2-0c02-412a-9550-83fcc1cbcee3\" class = \"xr-section-summary\">constant_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body[data-theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-summary-in + label:before {\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
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              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
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              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 174)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 166 167 168 169 170 171 172 173\n",
              "Data variables:\n",
              "    x        (obs_id) int32 38 43 31 35 45 42 41 58 ... 29 36 43 32 42 42 39 33\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:08:03.707926\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-e264ec57-0488-412d-90ad-8ed40b925e73' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e264ec57-0488-412d-90ad-8ed40b925e73' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 174</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-7b09d293-b0c4-4a68-8d61-cc0569076b8b' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7b09d293-b0c4-4a68-8d61-cc0569076b8b' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 169 170 171 172 173</div><input id='attrs-ffb35490-c3ff-41c2-b06f-41c04ba1f430' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ffb35490-c3ff-41c2-b06f-41c04ba1f430' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8e2410ba-970c-4ad3-baa1-08d3c4abd85c' class='xr-var-data-in' type='checkbox'><label for='data-8e2410ba-970c-4ad3-baa1-08d3c4abd85c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0dd5373e-f44d-47e7-a303-d213b14cda27' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0dd5373e-f44d-47e7-a303-d213b14cda27' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>38 43 31 35 45 ... 32 42 42 39 33</div><input id='attrs-c5b70f7f-97eb-46c2-bee8-dca3b5e58a0e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c5b70f7f-97eb-46c2-bee8-dca3b5e58a0e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-30cb773c-737f-497a-9bdc-4785877e91cf' class='xr-var-data-in' type='checkbox'><label for='data-30cb773c-737f-497a-9bdc-4785877e91cf' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([38, 43, 31, 35, 45, 42, 41, 58, 47, 33, 40, 34, 45, 38, 31, 40, 37,\n",
              "       36, 37, 38, 35, 34, 44, 44, 36, 36, 39, 40, 30, 47, 35, 48, 42, 42,\n",
              "       40, 35, 36, 28, 47, 27, 49, 41, 37, 37, 41, 49, 54, 50, 36, 43, 35,\n",
              "       33, 40, 39, 39, 46, 26, 49, 36, 42, 43, 33, 46, 46, 51, 43, 38, 44,\n",
              "       49, 26, 31, 50, 47, 42, 46, 36, 40, 33, 33, 50, 43, 30, 36, 37, 30,\n",
              "       42, 39, 46, 39, 28, 52, 26, 43, 38, 38, 46, 39, 44, 41, 44, 42, 30,\n",
              "       39, 45, 46, 38, 36, 42, 39, 41, 37, 32, 49, 40, 42, 43, 48, 47, 35,\n",
              "       44, 35, 48, 38, 45, 34, 30, 35, 45, 42, 32, 39, 38, 33, 35, 36, 36,\n",
              "       46, 43, 26, 34, 37, 44, 41, 50, 22, 43, 41, 57, 43, 45, 39, 43, 41,\n",
              "       57, 35, 43, 39, 38, 33, 55, 38, 46, 42, 48, 26, 40, 29, 36, 43, 32,\n",
              "       42, 42, 39, 33], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2e0d5fe8-7be9-4f25-a5da-387dcc703e81' class='xr-section-summary-in' type='checkbox'  checked><label for='section-2e0d5fe8-7be9-4f25-a5da-387dcc703e81' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:08:03.707926</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "              </ul>\n",
              "            </div>\n",
              "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-sections.group-sections {\n",
              "  grid-template-columns: auto;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt, dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              ".xr-wrap{width:700px!important;} </style>"
            ],
            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior_predictive\n",
              "\t> observed_data\n",
              "\t> constant_data"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ppc"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "id": "D4D12C8065F344968CABCEEDDA86140F",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "X为45时，Y是否超出后验预测HDI: False\n"
          ]
        }
      ],
      "source": [
        "# 定义函数，计算对应X下的观测值超出后验预测模型hdi范围的数量\n",
        "def count_outlier(i,hdi=0.94,ppc=ppc):\n",
        "  # 提取第i个X的值\n",
        "  X = ppc.constant_data[\"x\"][i].values\n",
        "  # 提取第i个X值对应的后验预测值\n",
        "  pre_ys = ppc.posterior_predictive[\"y_est\"].stack(sample=(\"chain\", \"draw\"))[i].values\n",
        "  # 提取对应X值下的观测值Y\n",
        "  true_ys = ppc.observed_data[\"y_est\"][i].values\n",
        "  \n",
        "  # 计算对应后验预测的hdi的上下限\n",
        "  lower,upper = az.hdi(pre_ys, hdi_prob=hdi)\n",
        "  \n",
        "  # 判断是否超过 hdi 边界\n",
        "  outlier = (true_ys > upper) | (true_ys < lower)\n",
        "\n",
        "  return outlier\n",
        "\n",
        "# 判断X为45时，对应的观测值Y是否超出后验预测HDI范围\n",
        "i = 123\n",
        "print(f\"X为{df.stress[i]}时，Y是否超出后验预测HDI:\", count_outlier(i))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BE2DD0B9EB4F43A78452DEC23F90D44E",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "* 通过一次定义，我们可以得到一个$X$下，其对应的观测值$Y$是否超出后验预测HDI。  \n",
        "\n",
        "* 我们可以通过循环，对每个$X$执行这个操作，再总结$Y$超出后验预测HDI的次数。"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "collapsed": false,
        "id": "C11E8ECBCB4246E8AD255A4642231A44",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "所有超过后验预测范围HDI的数量: 11\n"
          ]
        }
      ],
      "source": [
        "# 建立一个list,存储是否超过后验预测范围的判断结果\n",
        "hdi_verify = []\n",
        "\n",
        "# 使用循环，判断所有X对应的Y是否超出后验预测范围，并计数\n",
        "for i in range(len(df)):  \n",
        "  hdi_verify.append(count_outlier(i, hdi=0.94))\n",
        "total_number = sum(hdi_verify)\n",
        "\n",
        "\n",
        "print(f\"所有超过后验预测范围HDI的数量: {total_number}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3A33C9EBB1FE4112A109234BF08A26C4",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "* 考虑到我们一共有 174 个观测值，其中有11个观测值超过94%的后验预测HDI  \n",
        "\n",
        "* 这表明，我们的预测准确率超过 90%，$(174-11)/174 = 0.937$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "id": "4F147CE17CF24CF58811F76CAF36592F",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f47442f26a0>"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "text/html": [
              "<img src=\"https://cdn.kesci.com/upload/rt/90E00D15E9414EB5B69344C990188C14/s41cdlh0f8.png\">"
            ],
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# 可视化后验预测区间的结果\n",
        "az.plot_lm(idata=ppc,           # 传入后验预测的数据集\n",
        "           x='x',               # 传入ppc中，自变量的名称\n",
        "           y='y_est',           # 传入ppc中，观测变量的名称\n",
        "           kind_pp=\"hdi\",       # 绘制可信区间\n",
        "           kind_model=\"hdi\")\n",
        "plt.legend(loc=\"upper right\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "765B0BD7A15F474B853D34F8816BD1E9",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "### 练习一  \n",
        "观察不同HDI范围(例如hdi = 50%)下，超出后验预测范围观测值的数量。"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "collapsed": false,
        "id": "776CD7D70F964CC9AB3FBBEC7EBF36F3",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [],
      "source": [
        "# 建立一个list,存储是否超过后验预测范围的判断结果\n",
        "hdi_verify = []\n",
        "\n",
        "##================================================\n",
        "#                \n",
        "#                提示：通过向count_outlier中加入 hdi=0.5可以调整HDI的范围为50%\n",
        "#================================================\n",
        "\n",
        "# 使用循环，判断所有X对应的Y是否超出后验预测范围，并计数\n",
        "for i in range(...):  \n",
        "  hdi_verify.append(...)\n",
        "total_number = sum(...)\n",
        "\n",
        "\n",
        "print(f\"所有超过后验预测范围观测值的数量: {total_number}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false,
        "id": "53503588A8514A5E99A0C7275E555C2F",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [],
      "source": [
        "# 可视化后验预测区间的结果\n",
        "az.plot_lm(idata=ppc,           #传入后验预测的数据集\n",
        "           x='x',               #传入ppc中，自变量的名称\n",
        "           y='y_est',           #传入ppc中，观测变量的名称\n",
        "           kind_pp=\"hdi\",       #绘制可信区间\n",
        "           y_hat_fill_kwargs={\"hdi_prob\":0.5},\n",
        "           kind_model=\"hdi\")\n",
        "plt.legend(loc=\"upper right\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8EC1B486952E4686BC1AFB4478680E70",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "## 练习二: 当自变量为二分离散变量  \n",
        "\n",
        "### 目标：使用一个新的数据，完成线性模型的建立并完成本课的模型评估。  \n",
        "\n",
        "* 这里，我们考虑一个简单的二分变量*是否吸烟*，将其作为自变量，来预测*自我控制分数*  \n",
        "\t* 我们可以有个直觉的猜测：比如吸烟的个体自控力可能更差。"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "collapsed": false,
        "id": "096144C04E514A03B756E5F10A70CAF4",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [],
      "source": [
        "# 加载数据 Data_Sum_HPP_Multi_Site_Share.csv\n",
        "try:\n",
        "  df_raw = pd.read_csv('/home/mw/input/bayes20238001/Data_Sum_HPP_Multi_Site_Share.csv')\n",
        "except:\n",
        "  df_raw = pd.read_csv('data/Data_Sum_HPP_Multi_Site_Share.csv')\n",
        "\n",
        "# 筛选站点为\"METU\"的数据\n",
        "df_METU = df_raw[df_raw[\"Site\"] == \"...\"]\n",
        "\n",
        "# 选择需要的两列\n",
        "df_METU = df_METU[[\"scontrol\",\"smoke\"]]\n",
        "\n",
        "#1 表示抽烟，2表示不抽烟---重新编码---0 表示不抽烟，1表示抽烟\n",
        "df_METU[\"smoke\"] =  np.where(df_METU['smoke'] == 2, 0, 1)\n",
        "df_METU[\"smoke_recode\"] =  np.where(df_METU['smoke'] == 1, \"yes\", \"no\")\n",
        "\n",
        "#设置索引\n",
        "df_METU[\"index\"] = range(len(df_METU))\n",
        "df_METU = df_METU.set_index(\"index\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D7E9ECA9C9C1495093BA0C5D89DFF14A",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "* 在这个例子中，我们将是否吸烟作为自变量，将自我控制分数作为因变量  \n",
        "\n",
        "    * 在自变量中，`0` 表示不吸烟，`1`表示吸烟  \n",
        "\n",
        "$$  \n",
        "X_{i2} = \\begin{cases}  \n",
        "1 & \\text{Yes} \\\\  \n",
        "0 & \\text{No} \\\\  \n",
        "\\end{cases}  \n",
        "$$  \n",
        "\n",
        "简单画出两种情况下，自我控制分数分布的密度图  \n",
        "* 可见不吸烟的个体的自我控制得到分高于吸烟个体。  \n",
        "\n",
        "![Image Name](https://cdn.kesci.com/upload/s40nk3kagu.png?imageView2/0/w/960/h/960)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7C32EC6D76264E4482CB9CA83A0498D5",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "* 同样地，我们可以为抽烟和自我控制之间的关系建立一个正态回归模型：  \n",
        "\n",
        "$$\\begin{equation}  \n",
        "\\begin{array}{lcrl}  \n",
        "\\text{data:} & \\hspace{.05in} & Y_i|\\beta_0,\\beta_1,\\sigma & \\stackrel{ind}{\\sim} N(\\mu_i, \\; \\sigma^2) \\;\\; \\text{ with } \\;\\; \\mu_i = \\beta_0 + \\beta_1 X_{i2}\\\\  \n",
        "\\text{priors:} & & \\beta_{0}  &  \\sim N\\left(60, 2^2\\right)  \\\\  \n",
        "                     & & \\beta_1  & \\sim N\\left(-10, 4^2 \\right) \\\\  \n",
        "                     & & \\sigma & \\sim \\text{Exp}(0.6)  .\\\\  \n",
        "\\end{array}  \n",
        "\\end{equation}  \n",
        "$$  \n",
        "\n",
        "**在这个例子中，各参数的意义：**  \n",
        "\n",
        "* $\\beta_0  =  \\beta_0 + \\beta_1 \\cdot 0$  \n",
        "\n",
        "    * 当$X_{i2} = 0$时，$mu_i$的取值。 $\\beta_0$ 表示不抽烟情况下，自我控制分数的均值  \n",
        "\n",
        "* $\\beta_0 + \\beta_1 \\cdot 1 = \\beta_0 + \\beta_1$  \n",
        "\n",
        "    * $\\beta_1 $ ：当$X_{i2} = 1$时，$mu_i$的取值。表示抽烟情况下，自我控制分数的均值，则$\\beta_1 $表示了从不抽烟到抽烟，自我控制分数的变化程度  \n",
        "\n",
        "* 这里我们还是根据经验定义先验中的超参"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "335E719C643F41599A04F2217E81432B",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "**接下来我们直接运行模型定义、MCMC采样、后验预测部分**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "collapsed": false,
        "id": "5A5AF66FC9234DD08D62D44A553AEE62",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [],
      "source": [
        "with pm.Model() as category_model:\n",
        "\n",
        "    beta_0 = pm.Normal(\"beta_0\", mu= ..., sigma=...)      #定义beta_0          \n",
        "    beta_1 = pm.Normal(\"beta_1\", mu= ..., sigma=...)      #定义beta_1\n",
        "    sigma = pm.Exponential(\"sigma\", ...)                  #定义sigma\n",
        "\n",
        "    smoke = pm.MutableData(\"smoke\", df_METU.smoke, dims=\"obs_id\")\n",
        "    mu = pm.Deterministic(\"mu\", ..., dims=\"obs_id\")       #定义mu，线性回归中的关键\n",
        "\n",
        "    # 定义似然：预测值y符合N(mu, sigma)分布\n",
        "    # 通过 observed 传入实际数据y 自我控制水平\n",
        "    likelihood = pm.Normal(\"y_est\", mu=..., sigma=..., observed=..., dims=\"obs_id\")                                                                          "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "collapsed": false,
        "id": "39539125E3634EAE82C2821E897972C3",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
        },
        "tags": [],
        "trusted": true
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Auto-assigning NUTS sampler...\n",
            "Initializing NUTS using jitter+adapt_diag...\n",
            "Multiprocess sampling (4 chains in 4 jobs)\n",
            "NUTS: [beta_0, beta_1, sigma]\n"
          ]
        },
        {
          "data": {
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              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
              "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
              "    }\n",
              "</style>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 26 seconds.\n"
          ]
        }
      ],
      "source": [
        "#===========================\n",
        "#     用代码替代“...”\n",
        "#     注意！！！以下代码可能需要运行1-2分钟左右\n",
        "#===========================\n",
        "with ...:\n",
        "    cat_regression = ...(draws=5000,                   # 使用mcmc方法进行采样，draws为采样次数\n",
        "                      tune=1000,                    # tune为调整采样策略的次数，可以决定这些结果是否要被保留\n",
        "                      chains=4,                     # 链数\n",
        "                      discard_tuned_samples= True,  # tune的结果将在采样结束后被丢弃\n",
        "                      random_seed=84735)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
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        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
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        "tags": [],
        "trusted": true
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      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Sampling: [y_est]\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "<style>\n",
              "    /* Turns off some styling */\n",
              "    progress {\n",
              "        /* gets rid of default border in Firefox and Opera. */\n",
              "        border: none;\n",
              "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "        background-size: auto;\n",
              "    }\n",
              "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
              "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
              "    }\n",
              "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "        background: #F44336;\n",
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              "</style>\n"
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      ],
      "source": [
        "#===========================\n",
        "#     用代码替代“...”\n",
        "#===========================\n",
        "with ...:\n",
        "    cat_ppc = ...(cat_regression,\n",
        "                                             random_seed=84735) "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "84D0F597AFBC4ACBAD7331A6B185CF2B",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
          "execution_status": null,
          "is_visible": false,
          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "### 代码练习  \n",
        "\n",
        "* 我们以这个新模型为例，进行对MAE、后验预测区间代码的完整练习  \n",
        "\n",
        "* 结合之前的代码，对缺失的部分进行补充"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "collapsed": false,
        "id": "A7FE678C0EC045A6A133318227A57948",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
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        "tags": [],
        "trusted": true
      },
      "outputs": [
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              "\n",
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              "\n",
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              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 4, draw: 5000, obs_id: 181)\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1 2 3\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 4993 4994 4995 4996 4997 4998 4999\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    y_est    (chain, draw, obs_id) float64 39.14 19.25 53.65 ... 29.77 46.47\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.373214\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-70898167-d649-4b55-8782-ae2eeeaa94e5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-70898167-d649-4b55-8782-ae2eeeaa94e5' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-bc4f5942-4381-4eb4-a9b6-d4a7bc61ceaf' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bc4f5942-4381-4eb4-a9b6-d4a7bc61ceaf' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-0e54cb8f-5903-42e6-8f65-c2cf25a1eeaf' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0e54cb8f-5903-42e6-8f65-c2cf25a1eeaf' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-02acb295-0e64-454a-b9a7-9d52969fd326' class='xr-var-data-in' type='checkbox'><label for='data-02acb295-0e64-454a-b9a7-9d52969fd326' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-314e9ae8-a87b-4d82-ade1-f02133a6b6f0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-314e9ae8-a87b-4d82-ade1-f02133a6b6f0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c5a00775-b164-449b-a816-a10a51bb7748' class='xr-var-data-in' type='checkbox'><label for='data-c5a00775-b164-449b-a816-a10a51bb7748' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-9cd942ce-aa26-465c-aec0-31909337ac22' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9cd942ce-aa26-465c-aec0-31909337ac22' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f94f2e0d-9b3f-478a-88f9-54e433e03edd' class='xr-var-data-in' type='checkbox'><label for='data-f94f2e0d-9b3f-478a-88f9-54e433e03edd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-a293b403-5f24-4a65-9ea6-1c9a8aedd4f8' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a293b403-5f24-4a65-9ea6-1c9a8aedd4f8' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(chain, draw, obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.14 19.25 53.65 ... 29.77 46.47</div><input id='attrs-22c74852-6fc1-4226-a3f8-0e249496f285' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-22c74852-6fc1-4226-a3f8-0e249496f285' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-651dbd30-9330-4af9-892d-0fd54a442660' class='xr-var-data-in' type='checkbox'><label for='data-651dbd30-9330-4af9-892d-0fd54a442660' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[39.14036145, 19.24965014, 53.64902579, ..., 33.78990124,\n",
              "         59.6168722 , 50.75033494],\n",
              "        [41.77914558, 34.77692961, 36.10095686, ..., 67.69763541,\n",
              "         51.35034133, 44.52321311],\n",
              "        [66.87577976, 37.07865025, 29.9253953 , ..., 55.39140366,\n",
              "         59.0206096 , 45.6604954 ],\n",
              "        ...,\n",
              "        [32.38429513, 28.15524635, 43.1853272 , ..., 44.50081244,\n",
              "         36.81016533, 52.99222666],\n",
              "        [39.70426191, 42.0874609 , 51.58385542, ..., 54.27217666,\n",
              "         37.54478187, 41.60727793],\n",
              "        [46.86232552, 32.80944994, 41.73804239, ..., 48.07368946,\n",
              "         38.66885675, 42.33855684]],\n",
              "\n",
              "       [[33.70061543, 29.66849582, 38.99373278, ..., 49.60785837,\n",
              "         39.17289267, 25.43658143],\n",
              "        [38.37671117, 32.16479044, 46.68788758, ..., 44.80624871,\n",
              "         46.96206275, 42.48035583],\n",
              "        [51.12004893, 32.51432335, 54.34661136, ..., 45.21971557,\n",
              "         51.15870928, 41.20560365],\n",
              "...\n",
              "        [45.60102815, 34.75541529, 41.39049668, ..., 42.47836675,\n",
              "         44.87056757, 56.91171383],\n",
              "        [32.74748919, 37.5158197 , 34.83806795, ..., 38.33466792,\n",
              "         42.40535688, 41.59719164],\n",
              "        [52.76158067, 45.05880235, 35.54144862, ..., 43.98772723,\n",
              "         28.34818152, 60.08152021]],\n",
              "\n",
              "       [[45.32407116, 51.8702096 , 41.263651  , ..., 32.46561694,\n",
              "         39.15923431, 32.45162353],\n",
              "        [36.60244892, 23.61223192, 44.45267908, ..., 42.75318313,\n",
              "         23.51218872, 42.94780902],\n",
              "        [35.50479152, 28.91896565, 34.59633934, ..., 38.62803287,\n",
              "         55.45373101, 42.13736704],\n",
              "        ...,\n",
              "        [42.97133986, 43.09843745, 42.79008706, ..., 40.25323533,\n",
              "         39.53019916, 44.16610224],\n",
              "        [50.25162397, 43.1940362 , 44.56698078, ..., 64.163296  ,\n",
              "         30.45961875, 54.88605755],\n",
              "        [45.78029633, 41.34689505, 38.56318859, ..., 36.62434103,\n",
              "         29.77159954, 46.46546465]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-baf4cb30-9b47-4b4c-a9f0-0dcbfc0a9796' class='xr-section-summary-in' type='checkbox'  checked><label for='section-baf4cb30-9b47-4b4c-a9f0-0dcbfc0a9796' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.373214</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
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              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    y_est    (obs_id) float64 39.0 40.0 40.0 57.0 63.0 ... 43.0 38.0 31.0 45.0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.378281\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-bbef9716-8a4e-4138-bcac-253b0d6e2889' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-bbef9716-8a4e-4138-bcac-253b0d6e2889' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-c2f74634-fc83-4199-bb38-aed9cf5ee38f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c2f74634-fc83-4199-bb38-aed9cf5ee38f' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-87317e1f-6f06-4167-850c-b7b8b5f789c2' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-87317e1f-6f06-4167-850c-b7b8b5f789c2' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-849dcc35-bef6-499e-b820-72fed160a2d9' class='xr-var-data-in' type='checkbox'><label for='data-849dcc35-bef6-499e-b820-72fed160a2d9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-9e7b00df-1519-4e56-91c3-d4baeeaeffa3' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9e7b00df-1519-4e56-91c3-d4baeeaeffa3' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.0 40.0 40.0 ... 38.0 31.0 45.0</div><input id='attrs-e0c83acb-4e71-42c5-b799-5621960c774c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e0c83acb-4e71-42c5-b799-5621960c774c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6400ebfd-fb9e-4da4-8956-ef129d7f4656' class='xr-var-data-in' type='checkbox'><label for='data-6400ebfd-fb9e-4da4-8956-ef129d7f4656' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([39., 40., 40., 57., 63., 31., 40., 26., 36., 41., 35., 25., 45.,\n",
              "       50., 42., 40., 42., 45., 36., 49., 30., 49., 37., 51., 33., 43.,\n",
              "       31., 47., 39., 52., 30., 26., 28., 51., 56., 40., 46., 28., 35.,\n",
              "       37., 44., 35., 40., 54., 33., 33., 55., 30., 49., 34., 20., 34.,\n",
              "       49., 41., 47., 35., 50., 60., 43., 46., 47., 33., 42., 22., 36.,\n",
              "       35., 45., 37., 34., 43., 27., 47., 53., 48., 37., 32., 49., 48.,\n",
              "       38., 36., 47., 50., 55., 46., 30., 32., 43., 37., 31., 41., 33.,\n",
              "       23., 53., 38., 34., 48., 36., 40., 39., 31., 40., 28., 30., 49.,\n",
              "       52., 33., 39., 44., 24., 43., 48., 37., 46., 48., 41., 38., 30.,\n",
              "       36., 38., 34., 44., 30., 45., 51., 37., 42., 46., 51., 40., 43.,\n",
              "       42., 37., 30., 25., 47., 31., 25., 51., 38., 36., 36., 39., 51.,\n",
              "       41., 43., 49., 46., 25., 27., 43., 52., 33., 38., 35., 24., 42.,\n",
              "       34., 40., 37., 41., 48., 39., 42., 32., 59., 54., 51., 34., 37.,\n",
              "       39., 43., 47., 47., 38., 25., 28., 31., 43., 38., 31., 45.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-bd6e2b7e-bf97-4bb1-9e2e-b1fadbf406b0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-bd6e2b7e-bf97-4bb1-9e2e-b1fadbf406b0' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.378281</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_constant_data6a261bc9-aaf4-439e-a2df-1c9de592d701\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_constant_data6a261bc9-aaf4-439e-a2df-1c9de592d701\" class = \"xr-section-summary\">constant_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
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              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
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              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
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              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
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              "\n",
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              "  --xr-border-color: #1F1F1F;\n",
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              "  --xr-background-color-row-even: #111111;\n",
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              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
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              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
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              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
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              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
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              "\n",
              ".xr-obj-type {\n",
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              "\n",
              ".xr-sections {\n",
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              "  display: grid;\n",
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              "\n",
              ".xr-section-item {\n",
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              "\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
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              "\n",
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              "\n",
              ".xr-section-details {\n",
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              "\n",
              ".xr-array-wrap {\n",
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              "  display: grid;\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
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              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
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              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
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              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
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              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
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              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
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              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
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              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
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              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    smoke    (obs_id) int32 0 1 0 0 0 1 1 1 0 0 0 0 ... 0 0 0 0 1 0 0 0 0 0 0 0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.382856\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-9c934157-4a12-4806-af0d-523efddb19f5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-9c934157-4a12-4806-af0d-523efddb19f5' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-7c3c0a65-0b70-4cdb-8dfd-fc7f7eac9712' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7c3c0a65-0b70-4cdb-8dfd-fc7f7eac9712' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-d03d5f21-9586-4a87-ab75-ae49c429285e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d03d5f21-9586-4a87-ab75-ae49c429285e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3db7d55a-29df-4b35-896d-cb00bd6667d6' class='xr-var-data-in' type='checkbox'><label for='data-3db7d55a-29df-4b35-896d-cb00bd6667d6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e35232a5-78c4-4b3f-bef4-1f021997182e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e35232a5-78c4-4b3f-bef4-1f021997182e' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>smoke</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 0 0 0 1 1 1 ... 1 0 0 0 0 0 0 0</div><input id='attrs-2165af1d-2af8-49b5-b2ba-d39af91d10de' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2165af1d-2af8-49b5-b2ba-d39af91d10de' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-678de179-39a8-4201-aa4d-ae6a3c0c18dd' class='xr-var-data-in' type='checkbox'><label for='data-678de179-39a8-4201-aa4d-ae6a3c0c18dd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0,\n",
              "       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0,\n",
              "       1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0,\n",
              "       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1,\n",
              "       0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,\n",
              "       1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0c3cb89d-7262-455d-8016-397f47602af8' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0c3cb89d-7262-455d-8016-397f47602af8' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.382856</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "              </ul>\n",
              "            </div>\n",
              "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
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              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
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              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
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              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
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              "\n",
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              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
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              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-sections.group-sections {\n",
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              "\n",
              ".xr-section-item {\n",
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              "\n",
              ".xr-section-item input {\n",
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              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-item input:enabled + label {\n",
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              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              "\n",
              ".xr-section-summary {\n",
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              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
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              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
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              "  font-size: 11px;\n",
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              "  text-align: center;\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
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              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
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              "\n",
              ".xr-section-inline-details {\n",
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              "\n",
              ".xr-section-details {\n",
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              "  grid-column: 1 / -1;\n",
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              "\n",
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              "\n",
              ".xr-array-wrap {\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
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              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
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              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
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              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
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              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
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              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
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              "\n",
              ".xr-dim-list:before {\n",
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              "\n",
              ".xr-dim-list:after {\n",
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              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
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              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
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              "\n",
              ".xr-var-name {\n",
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              "\n",
              ".xr-var-dims {\n",
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              "\n",
              ".xr-var-dtype {\n",
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              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
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              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
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              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
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              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
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              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
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              "\n",
              ".xr-var-data > table {\n",
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              "\n",
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              "\n",
              ".xr-attrs,\n",
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              ".xr-var-data {\n",
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              "\n",
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              "\n",
              ".xr-attrs dt, dd {\n",
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              "\n",
              ".xr-attrs dt {\n",
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              "\n",
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            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior_predictive\n",
              "\t> observed_data\n",
              "\t> constant_data"
            ]
          },
          "execution_count": 37,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "cat_ppc"
      ]
    },
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      "source": [
        "### 计算MAE：  \n",
        "\n",
        "* 温馨提示：仔细查看上一行的`cat_ppc`中的各个变量，确保自己大致理解其中的含义"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      "source": [
        "##================================================\n",
        "#                练习，修改... 部分\n",
        "#                \n",
        "#================================================\n",
        "\n",
        "# 计算每个X取值下对应的后验预测模型的均值\n",
        "cat_pre_x = cat_ppc.posterior_predictive[...].stack(sample=(\"chain\", \"draw\"))\n",
        "cat_pre_y_mean = cat_pre_x.mean(axis=1).values\n",
        "\n",
        "# 提取对应X值下的观测值Y，提取对应X值下的后验预测模型的均值\n",
        "cat_MAE = pd.DataFrame({\n",
        "    \"smoke\": ...,\n",
        "    \"scontrol_ppc_mean\": ...,\n",
        "    \"scontrol_original\": ...\n",
        "})\n",
        "cat_MAE.head(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false,
        "id": "D9DF19E138A642A8A59012DA50475278",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
          "slide_type": "fragment"
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        "trusted": true
      },
      "outputs": [],
      "source": [
        "from statistics import median\n",
        "\n",
        "# 计算预测误差\n",
        "cat_MAE[\"pre_error\"] = cat_MAE[...] - cat_MAE[...]\n",
        "\n",
        "# 最后，计算预测误差的中位数\n",
        "MAE = median(cat_MAE.pre_error)\n",
        "print(f\"计算得到的MAE: {MAE:.2f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0D8BB6EF497C4F19B5DAAAE57E3E18E9",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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          "status": "default"
        },
        "scrolled": false,
        "slideshow": {
          "slide_type": "slide"
        },
        "tags": []
      },
      "source": [
        "### 计算后验预测区间"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
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              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 4, draw: 5000, obs_id: 181)\n",
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              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-a87a8277-c8c2-40be-bb0a-8f77c8f165ab' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-a87a8277-c8c2-40be-bb0a-8f77c8f165ab' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-67b5e6b1-959a-4bed-8a1f-4ed989769d76' class='xr-section-summary-in' type='checkbox'  checked><label for='section-67b5e6b1-959a-4bed-8a1f-4ed989769d76' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-46164c39-c439-4a93-b9d3-7818278b26fb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-46164c39-c439-4a93-b9d3-7818278b26fb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a07c8851-c2b2-4159-ae96-eaf18376d07e' class='xr-var-data-in' type='checkbox'><label for='data-a07c8851-c2b2-4159-ae96-eaf18376d07e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-35894f08-0c67-477d-a809-ba9dc96b5045' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-35894f08-0c67-477d-a809-ba9dc96b5045' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-94246aa8-dcc3-403e-a70f-0ffccbf33a9f' class='xr-var-data-in' type='checkbox'><label for='data-94246aa8-dcc3-403e-a70f-0ffccbf33a9f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-7fe7ae36-7d9f-43ba-a620-cabc3b479b73' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7fe7ae36-7d9f-43ba-a620-cabc3b479b73' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2c892d61-77aa-45f1-9c6f-2b6a4ba3e08d' class='xr-var-data-in' type='checkbox'><label for='data-2c892d61-77aa-45f1-9c6f-2b6a4ba3e08d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4e06e974-21e9-4dae-a253-060445112d4e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-4e06e974-21e9-4dae-a253-060445112d4e' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(chain, draw, obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.14 19.25 53.65 ... 29.77 46.47</div><input id='attrs-c0ec0253-9ba1-4b95-8cf3-bf77fa6e47dc' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c0ec0253-9ba1-4b95-8cf3-bf77fa6e47dc' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5225f65b-ac91-498c-a018-e7759fc93f6e' class='xr-var-data-in' type='checkbox'><label for='data-5225f65b-ac91-498c-a018-e7759fc93f6e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[39.14036145, 19.24965014, 53.64902579, ..., 33.78990124,\n",
              "         59.6168722 , 50.75033494],\n",
              "        [41.77914558, 34.77692961, 36.10095686, ..., 67.69763541,\n",
              "         51.35034133, 44.52321311],\n",
              "        [66.87577976, 37.07865025, 29.9253953 , ..., 55.39140366,\n",
              "         59.0206096 , 45.6604954 ],\n",
              "        ...,\n",
              "        [32.38429513, 28.15524635, 43.1853272 , ..., 44.50081244,\n",
              "         36.81016533, 52.99222666],\n",
              "        [39.70426191, 42.0874609 , 51.58385542, ..., 54.27217666,\n",
              "         37.54478187, 41.60727793],\n",
              "        [46.86232552, 32.80944994, 41.73804239, ..., 48.07368946,\n",
              "         38.66885675, 42.33855684]],\n",
              "\n",
              "       [[33.70061543, 29.66849582, 38.99373278, ..., 49.60785837,\n",
              "         39.17289267, 25.43658143],\n",
              "        [38.37671117, 32.16479044, 46.68788758, ..., 44.80624871,\n",
              "         46.96206275, 42.48035583],\n",
              "        [51.12004893, 32.51432335, 54.34661136, ..., 45.21971557,\n",
              "         51.15870928, 41.20560365],\n",
              "...\n",
              "        [45.60102815, 34.75541529, 41.39049668, ..., 42.47836675,\n",
              "         44.87056757, 56.91171383],\n",
              "        [32.74748919, 37.5158197 , 34.83806795, ..., 38.33466792,\n",
              "         42.40535688, 41.59719164],\n",
              "        [52.76158067, 45.05880235, 35.54144862, ..., 43.98772723,\n",
              "         28.34818152, 60.08152021]],\n",
              "\n",
              "       [[45.32407116, 51.8702096 , 41.263651  , ..., 32.46561694,\n",
              "         39.15923431, 32.45162353],\n",
              "        [36.60244892, 23.61223192, 44.45267908, ..., 42.75318313,\n",
              "         23.51218872, 42.94780902],\n",
              "        [35.50479152, 28.91896565, 34.59633934, ..., 38.62803287,\n",
              "         55.45373101, 42.13736704],\n",
              "        ...,\n",
              "        [42.97133986, 43.09843745, 42.79008706, ..., 40.25323533,\n",
              "         39.53019916, 44.16610224],\n",
              "        [50.25162397, 43.1940362 , 44.56698078, ..., 64.163296  ,\n",
              "         30.45961875, 54.88605755],\n",
              "        [45.78029633, 41.34689505, 38.56318859, ..., 36.62434103,\n",
              "         29.77159954, 46.46546465]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f930f2dc-0375-43c2-b275-a54563514f85' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f930f2dc-0375-43c2-b275-a54563514f85' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.373214</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
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              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    y_est    (obs_id) float64 39.0 40.0 40.0 57.0 63.0 ... 43.0 38.0 31.0 45.0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.378281\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-3a502a56-0a1f-4c6d-b8c6-175392cb091f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-3a502a56-0a1f-4c6d-b8c6-175392cb091f' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-65b83b60-53ce-47ec-9a33-0d4d6e11b669' class='xr-section-summary-in' type='checkbox'  checked><label for='section-65b83b60-53ce-47ec-9a33-0d4d6e11b669' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-a08f61d6-11a9-46b2-bdef-8321940a335b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a08f61d6-11a9-46b2-bdef-8321940a335b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-87bb0976-dd8b-45ad-82b9-0e5809d1695f' class='xr-var-data-in' type='checkbox'><label for='data-87bb0976-dd8b-45ad-82b9-0e5809d1695f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-a0994e20-3154-4b1f-ac8b-7ed405df07be' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a0994e20-3154-4b1f-ac8b-7ed405df07be' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.0 40.0 40.0 ... 38.0 31.0 45.0</div><input id='attrs-43d3ea15-788c-4839-8ad5-fae3babbe973' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-43d3ea15-788c-4839-8ad5-fae3babbe973' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-61625d21-cbfa-4bbd-9896-8467e9235d5a' class='xr-var-data-in' type='checkbox'><label for='data-61625d21-cbfa-4bbd-9896-8467e9235d5a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([39., 40., 40., 57., 63., 31., 40., 26., 36., 41., 35., 25., 45.,\n",
              "       50., 42., 40., 42., 45., 36., 49., 30., 49., 37., 51., 33., 43.,\n",
              "       31., 47., 39., 52., 30., 26., 28., 51., 56., 40., 46., 28., 35.,\n",
              "       37., 44., 35., 40., 54., 33., 33., 55., 30., 49., 34., 20., 34.,\n",
              "       49., 41., 47., 35., 50., 60., 43., 46., 47., 33., 42., 22., 36.,\n",
              "       35., 45., 37., 34., 43., 27., 47., 53., 48., 37., 32., 49., 48.,\n",
              "       38., 36., 47., 50., 55., 46., 30., 32., 43., 37., 31., 41., 33.,\n",
              "       23., 53., 38., 34., 48., 36., 40., 39., 31., 40., 28., 30., 49.,\n",
              "       52., 33., 39., 44., 24., 43., 48., 37., 46., 48., 41., 38., 30.,\n",
              "       36., 38., 34., 44., 30., 45., 51., 37., 42., 46., 51., 40., 43.,\n",
              "       42., 37., 30., 25., 47., 31., 25., 51., 38., 36., 36., 39., 51.,\n",
              "       41., 43., 49., 46., 25., 27., 43., 52., 33., 38., 35., 24., 42.,\n",
              "       34., 40., 37., 41., 48., 39., 42., 32., 59., 54., 51., 34., 37.,\n",
              "       39., 43., 47., 47., 38., 25., 28., 31., 43., 38., 31., 45.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-7e9921de-f17a-468e-8f81-c0393921a4a2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7e9921de-f17a-468e-8f81-c0393921a4a2' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.378281</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_constant_data4d350b47-0f2f-4981-87b6-bd5059b466dd\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_constant_data4d350b47-0f2f-4981-87b6-bd5059b466dd\" class = \"xr-section-summary\">constant_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
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              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
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              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
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              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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              "\n",
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              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
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              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
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              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
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              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
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              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
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              "\n",
              ".xr-section-item {\n",
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              "\n",
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              "\n",
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              "\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
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              "\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
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              "\n",
              ".xr-section-inline-details {\n",
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              "\n",
              ".xr-section-details {\n",
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              "\n",
              ".xr-array-wrap {\n",
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              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
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              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
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              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
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              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
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              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
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              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    smoke    (obs_id) int32 0 1 0 0 0 1 1 1 0 0 0 0 ... 0 0 0 0 1 0 0 0 0 0 0 0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.382856\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-c011e92b-f135-4ea8-9b82-b691a1f5770a' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-c011e92b-f135-4ea8-9b82-b691a1f5770a' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-beb03425-a5a3-4537-a903-3ef5809b66a1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-beb03425-a5a3-4537-a903-3ef5809b66a1' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-a239d8dd-e4eb-4799-89c9-7b7537fac088' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a239d8dd-e4eb-4799-89c9-7b7537fac088' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-945c61a5-b014-428f-8dd3-db08048da376' class='xr-var-data-in' type='checkbox'><label for='data-945c61a5-b014-428f-8dd3-db08048da376' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5d39c90c-084a-4993-a35a-262486d60319' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5d39c90c-084a-4993-a35a-262486d60319' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>smoke</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 0 0 0 1 1 1 ... 1 0 0 0 0 0 0 0</div><input id='attrs-49a5bad6-107a-40d5-9f99-517953641d78' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-49a5bad6-107a-40d5-9f99-517953641d78' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3393ff12-3c84-4fbe-b727-57d21858d074' class='xr-var-data-in' type='checkbox'><label for='data-3393ff12-3c84-4fbe-b727-57d21858d074' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0,\n",
              "       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0,\n",
              "       1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0,\n",
              "       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1,\n",
              "       0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,\n",
              "       1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0eb9dba8-06d0-4cb2-915e-f70b3205bd7b' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0eb9dba8-06d0-4cb2-915e-f70b3205bd7b' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.382856</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "              </ul>\n",
              "            </div>\n",
              "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-sections.group-sections {\n",
              "  grid-template-columns: auto;\n",
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              "\n",
              ".xr-section-item {\n",
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              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
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              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
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              "\n",
              ".xr-section-details {\n",
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              "  grid-column: 1 / -1;\n",
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              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
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              "\n",
              ".xr-array-wrap {\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
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              "\n",
              ".xr-preview {\n",
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              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
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              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
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              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
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              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
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              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
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              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
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              "\n",
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              "\n",
              ".xr-var-dims {\n",
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              "\n",
              ".xr-var-dtype {\n",
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              "  text-align: right;\n",
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              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
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              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
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              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
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              "\n",
              ".xr-var-attrs,\n",
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              "  background-color: var(--xr-background-color) !important;\n",
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              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
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              "\n",
              ".xr-var-data > table {\n",
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              "\n",
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              ".xr-var-data {\n",
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              "\n",
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              "\n",
              ".xr-attrs dt, dd {\n",
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              "\n",
              ".xr-attrs dt {\n",
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              "\n",
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              "\n",
              ".xr-attrs dd {\n",
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            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior_predictive\n",
              "\t> observed_data\n",
              "\t> constant_data"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "cat_ppc"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
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        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
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      "source": [
        "# 定义函数，计算对应X下的观测值超出后验预测模型hdi范围的数量\n",
        "def count_outlier(i,hdi=0.94,ppc=cat_ppc):\n",
        "  # 提取第i个X的值\n",
        "  X = ppc.constant_data[\"smoke\"][i].values\n",
        "  # 提取第i个X值对应的后验预测值\n",
        "  pre_ys = ppc.posterior_predictive[\"y_est\"].stack(sample=(\"chain\", \"draw\"))[i].values\n",
        "  # 提取对应X值下的观测值Y\n",
        "  true_ys = ppc.observed_data[\"y_est\"][i].values\n",
        "  \n",
        "  # 计算对应后验预测的hdi的上下限\n",
        "  lower,upper = az.hdi(pre_ys, hdi_prob=hdi)\n",
        "  \n",
        "  # 判断是否超过 hdi 边界\n",
        "  outlier = (true_ys > upper) | (true_ys < lower)\n",
        "\n",
        "  return outlier"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false,
        "id": "9D36838150744C539122AD18E7FC6A76",
        "jupyter": {},
        "notebookId": "655b69f19f41eb29b96aa410",
        "scrolled": false,
        "slideshow": {
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      },
      "outputs": [],
      "source": [
        "# 建立一个list,存储是否超过后验预测范围的判断结果\n",
        "hdi_verify = []\n",
        "\n",
        "# 使用循环，判断所有X对应的Y是否超出后验预测范围，并计数\n",
        "for i in range(len(df_METU)):  \n",
        "  hdi_verify.append(count_outlier(...))\n",
        "total_number = sum(...)\n",
        "\n",
        "print(f\"所有超过后验预测范围观测值的数量: {total_number}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
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        "slideshow": {
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        "trusted": true
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              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 4, draw: 5000, obs_id: 181)\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1 2 3\n",
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              "    y_est    (chain, draw, obs_id) float64 39.14 19.25 53.65 ... 29.77 46.47\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.373214\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-5b7925c8-410b-4a76-b424-c13ce48ec0dc' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5b7925c8-410b-4a76-b424-c13ce48ec0dc' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 5000</li><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-79cd7bb0-cc49-4b6d-bd66-7bf7152644c1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-79cd7bb0-cc49-4b6d-bd66-7bf7152644c1' class='xr-section-summary' >Coordinates: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-c0136212-1a2c-4933-8b1e-50de5510ce8d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c0136212-1a2c-4933-8b1e-50de5510ce8d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ed53a168-4b8a-4844-a455-bf195dde220e' class='xr-var-data-in' type='checkbox'><label for='data-ed53a168-4b8a-4844-a455-bf195dde220e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 4996 4997 4998 4999</div><input id='attrs-bdf01539-ed02-4859-ae29-f369a0381e18' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bdf01539-ed02-4859-ae29-f369a0381e18' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-54523438-2b1c-4a59-b359-3a43d9ed5d48' class='xr-var-data-in' type='checkbox'><label for='data-54523438-2b1c-4a59-b359-3a43d9ed5d48' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 4997, 4998, 4999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-207a18c1-c809-481c-9c03-937c4e6d00b3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-207a18c1-c809-481c-9c03-937c4e6d00b3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-224635c9-c252-4107-a40f-a9e86bcd9b7e' class='xr-var-data-in' type='checkbox'><label for='data-224635c9-c252-4107-a40f-a9e86bcd9b7e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-496ad408-5d56-4e7f-807e-791a54fdab29' class='xr-section-summary-in' type='checkbox'  checked><label for='section-496ad408-5d56-4e7f-807e-791a54fdab29' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(chain, draw, obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.14 19.25 53.65 ... 29.77 46.47</div><input id='attrs-9b586270-afcc-4b02-86c1-6326c305a9d0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9b586270-afcc-4b02-86c1-6326c305a9d0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ca5717f8-4901-4303-8294-af53249e0ba6' class='xr-var-data-in' type='checkbox'><label for='data-ca5717f8-4901-4303-8294-af53249e0ba6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[39.14036145, 19.24965014, 53.64902579, ..., 33.78990124,\n",
              "         59.6168722 , 50.75033494],\n",
              "        [41.77914558, 34.77692961, 36.10095686, ..., 67.69763541,\n",
              "         51.35034133, 44.52321311],\n",
              "        [66.87577976, 37.07865025, 29.9253953 , ..., 55.39140366,\n",
              "         59.0206096 , 45.6604954 ],\n",
              "        ...,\n",
              "        [32.38429513, 28.15524635, 43.1853272 , ..., 44.50081244,\n",
              "         36.81016533, 52.99222666],\n",
              "        [39.70426191, 42.0874609 , 51.58385542, ..., 54.27217666,\n",
              "         37.54478187, 41.60727793],\n",
              "        [46.86232552, 32.80944994, 41.73804239, ..., 48.07368946,\n",
              "         38.66885675, 42.33855684]],\n",
              "\n",
              "       [[33.70061543, 29.66849582, 38.99373278, ..., 49.60785837,\n",
              "         39.17289267, 25.43658143],\n",
              "        [38.37671117, 32.16479044, 46.68788758, ..., 44.80624871,\n",
              "         46.96206275, 42.48035583],\n",
              "        [51.12004893, 32.51432335, 54.34661136, ..., 45.21971557,\n",
              "         51.15870928, 41.20560365],\n",
              "...\n",
              "        [45.60102815, 34.75541529, 41.39049668, ..., 42.47836675,\n",
              "         44.87056757, 56.91171383],\n",
              "        [32.74748919, 37.5158197 , 34.83806795, ..., 38.33466792,\n",
              "         42.40535688, 41.59719164],\n",
              "        [52.76158067, 45.05880235, 35.54144862, ..., 43.98772723,\n",
              "         28.34818152, 60.08152021]],\n",
              "\n",
              "       [[45.32407116, 51.8702096 , 41.263651  , ..., 32.46561694,\n",
              "         39.15923431, 32.45162353],\n",
              "        [36.60244892, 23.61223192, 44.45267908, ..., 42.75318313,\n",
              "         23.51218872, 42.94780902],\n",
              "        [35.50479152, 28.91896565, 34.59633934, ..., 38.62803287,\n",
              "         55.45373101, 42.13736704],\n",
              "        ...,\n",
              "        [42.97133986, 43.09843745, 42.79008706, ..., 40.25323533,\n",
              "         39.53019916, 44.16610224],\n",
              "        [50.25162397, 43.1940362 , 44.56698078, ..., 64.163296  ,\n",
              "         30.45961875, 54.88605755],\n",
              "        [45.78029633, 41.34689505, 38.56318859, ..., 36.62434103,\n",
              "         29.77159954, 46.46546465]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-90e8410e-f4f9-4520-a377-3b8fd3a64603' class='xr-section-summary-in' type='checkbox'  checked><label for='section-90e8410e-f4f9-4520-a377-3b8fd3a64603' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.373214</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
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              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    y_est    (obs_id) float64 39.0 40.0 40.0 57.0 63.0 ... 43.0 38.0 31.0 45.0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.378281\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-7a02430a-3116-4016-8c1d-19e0b3c3866d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7a02430a-3116-4016-8c1d-19e0b3c3866d' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-c6489af9-2c71-4995-8463-eabb74b279a5' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c6489af9-2c71-4995-8463-eabb74b279a5' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-00c12dbe-cc74-4a57-b4e0-0611beedbc36' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-00c12dbe-cc74-4a57-b4e0-0611beedbc36' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c6bc22a4-da7f-4929-8da1-c65bdd0f17eb' class='xr-var-data-in' type='checkbox'><label for='data-c6bc22a4-da7f-4929-8da1-c65bdd0f17eb' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-d99570a1-1437-470d-ac55-1ebd9fd3b8c2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-d99570a1-1437-470d-ac55-1ebd9fd3b8c2' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>y_est</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>39.0 40.0 40.0 ... 38.0 31.0 45.0</div><input id='attrs-363bf7b9-cd9c-40fe-a262-fb11d708e013' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-363bf7b9-cd9c-40fe-a262-fb11d708e013' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e748e0b3-2778-4607-80c9-e42070b172ad' class='xr-var-data-in' type='checkbox'><label for='data-e748e0b3-2778-4607-80c9-e42070b172ad' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([39., 40., 40., 57., 63., 31., 40., 26., 36., 41., 35., 25., 45.,\n",
              "       50., 42., 40., 42., 45., 36., 49., 30., 49., 37., 51., 33., 43.,\n",
              "       31., 47., 39., 52., 30., 26., 28., 51., 56., 40., 46., 28., 35.,\n",
              "       37., 44., 35., 40., 54., 33., 33., 55., 30., 49., 34., 20., 34.,\n",
              "       49., 41., 47., 35., 50., 60., 43., 46., 47., 33., 42., 22., 36.,\n",
              "       35., 45., 37., 34., 43., 27., 47., 53., 48., 37., 32., 49., 48.,\n",
              "       38., 36., 47., 50., 55., 46., 30., 32., 43., 37., 31., 41., 33.,\n",
              "       23., 53., 38., 34., 48., 36., 40., 39., 31., 40., 28., 30., 49.,\n",
              "       52., 33., 39., 44., 24., 43., 48., 37., 46., 48., 41., 38., 30.,\n",
              "       36., 38., 34., 44., 30., 45., 51., 37., 42., 46., 51., 40., 43.,\n",
              "       42., 37., 30., 25., 47., 31., 25., 51., 38., 36., 36., 39., 51.,\n",
              "       41., 43., 49., 46., 25., 27., 43., 52., 33., 38., 35., 24., 42.,\n",
              "       34., 40., 37., 41., 48., 39., 42., 32., 59., 54., 51., 34., 37.,\n",
              "       39., 43., 47., 47., 38., 25., 28., 31., 43., 38., 31., 45.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f0eb3e0e-2b45-4401-bb35-ae255d24b2ad' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f0eb3e0e-2b45-4401-bb35-ae255d24b2ad' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.378281</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_constant_data4dcc4b54-3984-43a0-9cf5-9843b252bc5b\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_constant_data4dcc4b54-3984-43a0-9cf5-9843b252bc5b\" class = \"xr-section-summary\">constant_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
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              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
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              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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              "\n",
              "html[theme=dark],\n",
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              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
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              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
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              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
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              "\n",
              ".xr-section-item input {\n",
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              "\n",
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              "\n",
              ".xr-section-item input:enabled + label {\n",
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              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              ".xr-section-summary {\n",
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              "\n",
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              "\n",
              ".xr-section-summary-in:disabled + label {\n",
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              "\n",
              ".xr-section-summary-in + label:before {\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
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              "\n",
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              "  display: none;\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
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              "\n",
              ".xr-section-inline-details {\n",
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              "\n",
              ".xr-section-details {\n",
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              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
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              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
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              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
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              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
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              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (obs_id: 181)\n",
              "Coordinates:\n",
              "  * obs_id   (obs_id) int64 0 1 2 3 4 5 6 7 ... 173 174 175 176 177 178 179 180\n",
              "Data variables:\n",
              "    smoke    (obs_id) int32 0 1 0 0 0 1 1 1 0 0 0 0 ... 0 0 0 0 1 0 0 0 0 0 0 0\n",
              "Attributes:\n",
              "    created_at:                 2023-11-13T00:44:30.382856\n",
              "    arviz_version:              0.16.0\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  5.6.0</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-23b43252-5021-487b-a4c5-e23bddb3236d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-23b43252-5021-487b-a4c5-e23bddb3236d' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>obs_id</span>: 181</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-a3758f3a-3f43-4b06-ade5-04fd662387a1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a3758f3a-3f43-4b06-ade5-04fd662387a1' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>obs_id</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 176 177 178 179 180</div><input id='attrs-ab74a8e1-ea3a-4d33-ad8d-98965c9abbd1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ab74a8e1-ea3a-4d33-ad8d-98965c9abbd1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0295b3de-6faa-4324-8157-c2e9bff3372e' class='xr-var-data-in' type='checkbox'><label for='data-0295b3de-6faa-4324-8157-c2e9bff3372e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
              "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
              "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
              "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
              "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
              "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
              "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
              "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
              "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
              "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
              "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
              "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
              "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1a82aac2-f335-4939-a0e8-336d5b39ae3c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1a82aac2-f335-4939-a0e8-336d5b39ae3c' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>smoke</span></div><div class='xr-var-dims'>(obs_id)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>0 1 0 0 0 1 1 1 ... 1 0 0 0 0 0 0 0</div><input id='attrs-16a1c925-6181-4c2d-938b-e9f55d686ff6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-16a1c925-6181-4c2d-938b-e9f55d686ff6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-53b26310-b596-436c-9c09-5da1609eb9ae' class='xr-var-data-in' type='checkbox'><label for='data-53b26310-b596-436c-9c09-5da1609eb9ae' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0,\n",
              "       0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0,\n",
              "       1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0,\n",
              "       1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0,\n",
              "       0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1,\n",
              "       0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0,\n",
              "       1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,\n",
              "       0, 0, 0, 0, 0], dtype=int32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c881eb53-d521-4897-a619-809a2835a629' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c881eb53-d521-4897-a619-809a2835a629' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2023-11-13T00:44:30.382856</dd><dt><span>arviz_version :</span></dt><dd>0.16.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.6.0</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "              </ul>\n",
              "            </div>\n",
              "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
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              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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              "\n",
              ".xr-sections.group-sections {\n",
              "  grid-template-columns: auto;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
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              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
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              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
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              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
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              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
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              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
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              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
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              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
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              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
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              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
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              "\n",
              ".xr-array-wrap {\n",
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              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
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              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
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              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
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              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
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              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
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              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
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              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
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              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
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              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
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              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
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              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
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              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
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              "  width: auto;\n",
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              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
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              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
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              "\n",
              ".xr-var-data > table {\n",
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              "\n",
              ".xr-var-name span,\n",
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              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
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              "\n",
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              "  margin: 0;\n",
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              "\n",
              ".xr-attrs dt, dd {\n",
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              "\n",
              ".xr-attrs dt {\n",
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              "\n",
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              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              ".xr-wrap{width:700px!important;} </style>"
            ],
            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior_predictive\n",
              "\t> observed_data\n",
              "\t> constant_data"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "cat_ppc"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "az.plot_lm(idata=...,           #传入后验预测的数据集\n",
        "           x=\"...\",             #传入ppc中，自变量的名称\n",
        "           y=\"...\",             #传入ppc中，观测变量的名称\n",
        "           kind_pp=\"hdi\",       #绘制可信区间\n",
        "           kind_model=\"hdi\",\n",
        "           y_kwargs={\"alpha\":0.5})\n",
        "plt.legend(loc='upper right')\n",
        "plt.xticks([0,1],[\"no\",\"yes\"],fontsize=15)\n",
        "plt.yticks(fontsize=15)\n",
        "plt.ylabel(\"Self control\",fontsize=16)\n",
        "plt.xlabel(\"Smoke\",fontsize=16)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "176D85859A004A0A9B12516FB09957F3",
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        },
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        "tags": []
      },
      "source": [
        "## 总结  \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6800B6BCEDEB4C1C9D07A88774E53236",
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        "notebookId": "655b69f19f41eb29b96aa410",
        "runtime": {
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        },
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      },
      "source": [
        "本节课讨论了模型的公平性和模型错误程度的话题。更重要的是结合后验预测检查和后验预测准确性来判断模型的预测效果。  \n",
        "       \n",
        "- 为了确定模型的后验预测准确性，我们计算两个重要的指标：  \n",
        "    \n",
        "    - 绝对误差的中位数，median absolute error (MAE)  \n",
        "    - 后验预测区间(posterior prediction interval)  \n",
        "\n",
        "- 此外，我们介绍了自变量为离散变量的回归模型，并进行了练习。  \n",
        "\t- 🤔一个值得思考的问题是：对于吸烟的个体，他们的压力是否更大，是否因为压力更大而导致自我控制力低？  \n",
        "\t- 下节课我们将探索这个问题。"
      ]
    }
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